Abstract group data - 1600.9849

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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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 40, 'aut_gen_orders': [8, 4, 10, 4, 4, 4], 'aut_gens': [[1, 2, 8, 80], [652, 1474, 1173, 1072], [1320, 978, 165, 608], [677, 1106, 648, 1520], [1013, 1570, 1132, 448], [520, 626, 485, 944], [801, 274, 188, 448]], 'aut_group': None, 'aut_hash': 7451043522633623305, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 25600, 'aut_permdeg': 80, 'aut_perms': [11331619615196703368223020843559194144183920420287728302758263607953000779051748587079127052525171148677696924753212126, 351202406359728528431064974604597020202148024162088333232165583508361849849120860420948375261938750039666342421417412, 51100518243392267608136837532436401136355470594954036482112656807973085777075150932500488136728573320091247883549288898, 47209684777133751154323504589934847905579111287446534363444869947131046540868529507562673881435699678031848356527515946, 20654219346790591027378064612021833194622392594442944866649373300491947118403357709127493806881366617359483389984502004, 5234490320005710953531579204795897258406090166561480642231057946619910858927204988693510083006719774551417401507147944], 'aut_phi_ratio': 40.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 4, 1], [2, 20, 2, 1], [2, 25, 1, 2], [4, 2, 1, 1], [4, 20, 2, 1], [4, 50, 1, 1], [4, 50, 2, 3], [4, 100, 1, 1], [4, 100, 4, 1], [5, 8, 1, 1], [5, 8, 2, 1], [10, 8, 1, 1], [10, 8, 2, 1], [10, 40, 4, 1], [10, 80, 2, 1], [20, 8, 4, 1], [20, 16, 1, 1], [20, 40, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5:D_5.C_2^5.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 40, 'autcentquo_group': '1600.10254', 'autcentquo_hash': 10254, 'autcentquo_nilpotent': False, 'autcentquo_order': 1600, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_5^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 10, 4], [2, 20, 2], [2, 25, 2], [4, 2, 1], [4, 20, 2], [4, 50, 7], [4, 100, 5], [5, 8, 3], [10, 8, 3], [10, 40, 4], [10, 80, 2], [20, 8, 4], [20, 16, 1], [20, 40, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '800.1194', 'commutator_count': 1, 'commutator_label': '100.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 9849, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 10, 1, 4], [2, 20, 1, 2], [2, 25, 1, 2], [4, 2, 1, 1], [4, 20, 1, 2], [4, 50, 1, 3], [4, 50, 2, 2], [4, 100, 1, 5], [5, 8, 1, 3], [10, 8, 1, 3], [10, 40, 1, 4], [10, 80, 1, 2], [20, 8, 2, 2], [20, 16, 1, 1], [20, 40, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 78744960, 'exponent': 20, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 0, 8], [16, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '800.1194', 'hash': 9849, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 10, 10], 'inner_gens': [[1, 2, 12, 464], [1, 2, 344, 240], [341, 1346, 8, 720], [1297, 1442, 968, 80]], 'inner_hash': 1194, 'inner_nilpotent': False, 'inner_order': 800, 'inner_split': True, 'inner_tex': 'D_5^2.C_2^3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 8], [4, 1], [8, 20], [16, 1]], 'label': '1600.9849', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'D5wrC2:D4', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 46, 'number_divisions': 40, 'number_normal_subgroups': 86, 'number_subgroup_autclasses': 190, 'number_subgroup_classes': 431, 'number_subgroups': 6278, 'old_label': None, 'order': 1600, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 131], [4, 892], [5, 24], [10, 344], [20, 208]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [400, 0, 0, 4], 'outer_gens': [[1, 402, 8, 80], [801, 2, 1352, 720], [801, 2, 808, 80], [680, 802, 33, 1088]], 'outer_group': '32.22', 'outer_hash': 22, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 16, 'outer_perms': [4396538203938, 123744649, 1327912203241, 14199841628278], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [4, 3], [8, 12], [16, 5]], 'representations': {'PC': {'code': 130777353315219827294424333965969697797599129951303858931734967339283337520695869635, 'gens': [1, 2, 4, 6], 'pres': [8, 2, 2, 2, 2, 5, 2, 2, 5, 41, 387, 5515, 10835, 91, 12804, 972, 660, 22277, 5773, 8661, 4349, 141, 47494, 13454, 20182, 10110, 166, 1031, 30735, 20503, 10271]}, 'Perm': {'d': 14, 'gens': [6370011487, 55693441, 6399067680, 17, 218912400, 7, 13990168200, 20855248560]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_5\\wr C_2:D_4', 'transitive_degree': 40, '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: 123279070
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 9849, 'group_order': 1600, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
  • id: 123279081
    {'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 9849, 'group_order': 1600, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 800, 'size': 1}
  • id: 123279092
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 3, 'group_counter': 9849, 'group_order': 1600, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 40, 'size': 10}
  • id: 123279103
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 4, 'group_counter': 9849, 'group_order': 1600, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 200, 'size': 10}
  • id: 123279111
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 5, 'group_counter': 9849, 'group_order': 1600, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 993, 'size': 10}
  • id: 123279112
    {'aut_label': '2B', 'centralizer': '10.a1', 'counter': 6, 'group_counter': 9849, 'group_order': 1600, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 497, 'size': 10}
  • id: 123279113
    {'aut_label': '2F', 'centralizer': '20.c1', 'counter': 7, 'group_counter': 9849, 'group_order': 1600, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 399, 'size': 20}
  • id: 123279114
    {'aut_label': '2F', 'centralizer': '20.c1', 'counter': 8, 'group_counter': 9849, 'group_order': 1600, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 907, 'size': 20}
  • id: 123279115
    {'aut_label': '2H', 'centralizer': '25.a1', 'counter': 9, 'group_counter': 9849, 'group_order': 1600, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 980, 'size': 25}
  • id: 123279071
    {'aut_label': '2I', 'centralizer': '25.a1', 'counter': 10, 'group_counter': 9849, 'group_order': 1600, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 804, 'size': 25}
  • id: 123279072
    {'aut_label': '4A', 'centralizer': '2.e1', 'counter': 11, 'group_counter': 9849, 'group_order': 1600, 'label': '4A', 'order': 4, 'powers': [2, 11], 'representative': 400, 'size': 2}
  • id: 123279073
    {'aut_label': '4B', 'centralizer': '20.a1', 'counter': 12, 'group_counter': 9849, 'group_order': 1600, 'label': '4B', 'order': 4, 'powers': [2, 12], 'representative': 120, 'size': 20}
  • id: 123279074
    {'aut_label': '4B', 'centralizer': '20.a1', 'counter': 13, 'group_counter': 9849, 'group_order': 1600, 'label': '4C', 'order': 4, 'powers': [2, 13], 'representative': 1089, 'size': 20}
  • id: 123279075
    {'aut_label': '4D', 'centralizer': '50.g1', 'counter': 14, 'group_counter': 9849, 'group_order': 1600, 'label': '4D', 'order': 4, 'powers': [9, 14], 'representative': 1033, 'size': 50}
  • id: 123279076
    {'aut_label': '4E', 'centralizer': '50.e1', 'counter': 15, 'group_counter': 9849, 'group_order': 1600, 'label': '4E', 'order': 4, 'powers': [2, 15], 'representative': 900, 'size': 50}
  • id: 123279077
    {'aut_label': '4D', 'centralizer': '50.g1', 'counter': 16, 'group_counter': 9849, 'group_order': 1600, 'label': '4F', 'order': 4, 'powers': [9, 16], 'representative': 185, 'size': 50}
  • id: 123279078
    {'aut_label': '4G1', 'centralizer': '50.d1', 'counter': 17, 'group_counter': 9849, 'group_order': 1600, 'label': '4G1', 'order': 4, 'powers': [9, 17], 'representative': 1106, 'size': 50}
  • id: 123279079
    {'aut_label': '4G-1', 'centralizer': '50.d1', 'counter': 18, 'group_counter': 9849, 'group_order': 1600, 'label': '4G-1', 'order': 4, 'powers': [9, 18], 'representative': 758, 'size': 50}
  • id: 123279080
    {'aut_label': '4G-1', 'centralizer': '50.d1', 'counter': 19, 'group_counter': 9849, 'group_order': 1600, 'label': '4H1', 'order': 4, 'powers': [9, 19], 'representative': 1158, 'size': 50}
  • id: 123279082
    {'aut_label': '4G1', 'centralizer': '50.d1', 'counter': 20, 'group_counter': 9849, 'group_order': 1600, 'label': '4H-1', 'order': 4, 'powers': [9, 20], 'representative': 1506, 'size': 50}
  • id: 123279083
    {'aut_label': '4I', 'centralizer': '100.d1', 'counter': 21, 'group_counter': 9849, 'group_order': 1600, 'label': '4I', 'order': 4, 'powers': [9, 21], 'representative': 586, 'size': 100}
  • id: 123279084
    {'aut_label': '4I', 'centralizer': '100.d1', 'counter': 22, 'group_counter': 9849, 'group_order': 1600, 'label': '4J', 'order': 4, 'powers': [9, 22], 'representative': 330, 'size': 100}
  • id: 123279085
    {'aut_label': '4K', 'centralizer': '100.j1', 'counter': 23, 'group_counter': 9849, 'group_order': 1600, 'label': '4K', 'order': 4, 'powers': [10, 23], 'representative': 281, 'size': 100}
  • id: 123279086
    {'aut_label': '4I', 'centralizer': '100.d1', 'counter': 24, 'group_counter': 9849, 'group_order': 1600, 'label': '4L', 'order': 4, 'powers': [9, 24], 'representative': 387, 'size': 100}
  • id: 123279087
    {'aut_label': '4I', 'centralizer': '100.d1', 'counter': 25, 'group_counter': 9849, 'group_order': 1600, 'label': '4M', 'order': 4, 'powers': [9, 25], 'representative': 291, 'size': 100}
  • id: 123279088
    {'aut_label': '5A', 'centralizer': '8.j1', 'counter': 26, 'group_counter': 9849, 'group_order': 1600, 'label': '5A', 'order': 5, 'powers': [26, 1], 'representative': 16, 'size': 8}
  • id: 123279089
    {'aut_label': '5A', 'centralizer': '8.j1', 'counter': 27, 'group_counter': 9849, 'group_order': 1600, 'label': '5B', 'order': 5, 'powers': [27, 1], 'representative': 336, 'size': 8}
  • id: 123279090
    {'aut_label': '5C', 'centralizer': '8.l1', 'counter': 28, 'group_counter': 9849, 'group_order': 1600, 'label': '5C', 'order': 5, 'powers': [28, 1], 'representative': 368, 'size': 8}
  • id: 123279091
    {'aut_label': '10A', 'centralizer': '8.j1', 'counter': 29, 'group_counter': 9849, 'group_order': 1600, 'label': '10A', 'order': 10, 'powers': [26, 2], 'representative': 160, 'size': 8}
  • id: 123279093
    {'aut_label': '10A', 'centralizer': '8.j1', 'counter': 30, 'group_counter': 9849, 'group_order': 1600, 'label': '10B', 'order': 10, 'powers': [27, 2], 'representative': 192, 'size': 8}
  • id: 123279094
    {'aut_label': '10C', 'centralizer': '8.l1', 'counter': 31, 'group_counter': 9849, 'group_order': 1600, 'label': '10C', 'order': 10, 'powers': [28, 2], 'representative': 224, 'size': 8}
  • id: 123279095
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 32, 'group_counter': 9849, 'group_order': 1600, 'label': '10D', 'order': 10, 'powers': [26, 3], 'representative': 8, 'size': 40}
  • id: 123279096
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 33, 'group_counter': 9849, 'group_order': 1600, 'label': '10E', 'order': 10, 'powers': [26, 4], 'representative': 168, 'size': 40}
  • id: 123279097
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 34, 'group_counter': 9849, 'group_order': 1600, 'label': '10F', 'order': 10, 'powers': [27, 5], 'representative': 321, 'size': 40}
  • id: 123279098
    {'aut_label': '10D', 'centralizer': '40.a1', 'counter': 35, 'group_counter': 9849, 'group_order': 1600, 'label': '10G', 'order': 10, 'powers': [27, 6], 'representative': 161, 'size': 40}
  • id: 123279099
    {'aut_label': '10H', 'centralizer': '80.c1', 'counter': 36, 'group_counter': 9849, 'group_order': 1600, 'label': '10H', 'order': 10, 'powers': [28, 7], 'representative': 47, 'size': 80}
  • id: 123279100
    {'aut_label': '10H', 'centralizer': '80.c1', 'counter': 37, 'group_counter': 9849, 'group_order': 1600, 'label': '10I', 'order': 10, 'powers': [28, 8], 'representative': 619, 'size': 80}
  • id: 123279101
    {'aut_label': '20A1', 'centralizer': '8.j1', 'counter': 38, 'group_counter': 9849, 'group_order': 1600, 'label': '20A1', 'order': 20, 'powers': [29, 11], 'representative': 80, 'size': 8}
  • id: 123279102
    {'aut_label': '20A1', 'centralizer': '8.j1', 'counter': 39, 'group_counter': 9849, 'group_order': 1600, 'label': '20A-1', 'order': 20, 'powers': [29, 11], 'representative': 1040, 'size': 8}
  • id: 123279104
    {'aut_label': '20A1', 'centralizer': '8.j1', 'counter': 40, 'group_counter': 9849, 'group_order': 1600, 'label': '20B1', 'order': 20, 'powers': [30, 11], 'representative': 96, 'size': 8}
  • id: 123279105
    {'aut_label': '20A1', 'centralizer': '8.j1', 'counter': 41, 'group_counter': 9849, 'group_order': 1600, 'label': '20B-1', 'order': 20, 'powers': [30, 11], 'representative': 1072, 'size': 8}
  • id: 123279106
    {'aut_label': '20C', 'centralizer': '16.b1', 'counter': 42, 'group_counter': 9849, 'group_order': 1600, 'label': '20C', 'order': 20, 'powers': [31, 11], 'representative': 112, 'size': 16}
  • id: 123279107
    {'aut_label': '20D1', 'centralizer': '40.a1', 'counter': 43, 'group_counter': 9849, 'group_order': 1600, 'label': '20D1', 'order': 20, 'powers': [29, 12], 'representative': 88, 'size': 40}
  • id: 123279108
    {'aut_label': '20D1', 'centralizer': '40.a1', 'counter': 44, 'group_counter': 9849, 'group_order': 1600, 'label': '20D-1', 'order': 20, 'powers': [29, 12], 'representative': 248, 'size': 40}
  • id: 123279109
    {'aut_label': '20D1', 'centralizer': '40.a1', 'counter': 45, 'group_counter': 9849, 'group_order': 1600, 'label': '20E1', 'order': 20, 'powers': [30, 13], 'representative': 81, 'size': 40}
  • id: 123279110
    {'aut_label': '20D1', 'centralizer': '40.a1', 'counter': 46, 'group_counter': 9849, 'group_order': 1600, 'label': '20E-1', 'order': 20, 'powers': [30, 13], 'representative': 1041, 'size': 40}
• 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: 7412367
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1a', '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], 'schur_index': 1}
  • id: 7412378
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1b', '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], 'schur_index': 1}
  • id: 7412389
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1c', '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], 'schur_index': 1}
  • id: 7412400
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1d', '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], 'schur_index': 1}
  • id: 7412402
    {'cdim': 1, 'counter': 5, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1e', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 7412403
    {'cdim': 1, 'counter': 6, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1f', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1], 'schur_index': 1}
  • id: 7412404
    {'cdim': 1, 'counter': 7, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1g', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 7412405
    {'cdim': 1, 'counter': 8, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1h', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1], 'schur_index': 1}
  • id: 7412406
    {'cdim': 1, 'counter': 9, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1i', '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], 'schur_index': 1}
  • id: 7412368
    {'cdim': 1, 'counter': 10, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1j', '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], 'schur_index': 1}
  • id: 7412369
    {'cdim': 1, 'counter': 11, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1k', '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], 'schur_index': 1}
  • id: 7412370
    {'cdim': 1, 'counter': 12, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1l', '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], 'schur_index': 1}
  • id: 7412371
    {'cdim': 1, 'counter': 13, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1m', '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], 'schur_index': 1}
  • id: 7412372
    {'cdim': 1, 'counter': 14, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1n', '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], 'schur_index': 1}
  • id: 7412373
    {'cdim': 1, 'counter': 15, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1o', '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], 'schur_index': 1}
  • id: 7412374
    {'cdim': 1, 'counter': 16, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.1p', '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], 'schur_index': 1}
  • id: 7412375
    {'cdim': 2, 'counter': 17, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2a', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, -2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412376
    {'cdim': 2, 'counter': 18, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2b', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412377
    {'cdim': 2, 'counter': 19, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2c', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412379
    {'cdim': 2, 'counter': 20, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2d', 'multiplicity': 1, 'nt': [4, 3], 'qdim': 2, 'qvalues': [2, -2, 2, -2, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412380
    {'cdim': 2, 'counter': 21, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2e', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412381
    {'cdim': 2, 'counter': 22, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.2f', 'multiplicity': 2, 'nt': [8, 11], 'qdim': 4, 'qvalues': [4, 4, 0, 0, 0, 0, 0, 0, -4, -4, 4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412382
    {'cdim': 4, 'counter': 23, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.4a', 'multiplicity': 1, 'nt': [16, 20], 'qdim': 4, 'qvalues': [4, -4, 0, 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 2}
  • id: 7412383
    {'cdim': 8, 'counter': 24, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8a', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 4, 4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, 0, 0, 0, 0, -1, -1, -2, -2, -2, -2, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412384
    {'cdim': 8, 'counter': 25, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8b', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 4, 4, 0, 0, 0, 0, 8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, 3, -2, -1, 0, -1, 0, 0, 0, -2, -2, 3, 3, -2, 0, -1, 0, -1], 'schur_index': 1}
  • id: 7412385
    {'cdim': 8, 'counter': 26, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8c', 'multiplicity': 1, 'nt': [10, 27], 'qdim': 8, 'qvalues': [8, 8, 4, 4, 0, 0, 0, 0, 0, 0, 8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, -1, 0, -1, 0, 0, 3, 3, -2, -2, -2, -1, 0, -1, 0], 'schur_index': 1}
  • id: 7412386
    {'cdim': 8, 'counter': 27, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8d', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, -4, -4, 0, 0, 0, 0, 0, 0, 8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, 1, 0, 1, 0, 0, 3, 3, -2, -2, -2, 1, 0, 1, 0], 'schur_index': 1}
  • id: 7412387
    {'cdim': 8, 'counter': 28, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8e', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -4, -4, 0, 0, 0, 0, 8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, 3, -2, 1, 0, 1, 0, 0, 0, -2, -2, 3, 3, -2, 0, 1, 0, 1], 'schur_index': 1}
  • id: 7412388
    {'cdim': 8, 'counter': 29, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8f', 'multiplicity': 1, 'nt': [20, 90], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, -4, -4, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, 0, 0, 0, 0, 1, 1, -2, -2, -2, -2, 3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412390
    {'cdim': 8, 'counter': 30, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8g', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, -4, -4, 0, 0, 0, 0, 0, 0, -8, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, 1, 0, 1, 0, 0, -3, -3, 2, 2, 2, -1, 0, -1, 0], 'schur_index': 1}
  • id: 7412391
    {'cdim': 8, 'counter': 31, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8h', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, 0, 0, -4, -4, 0, 0, 0, 0, -8, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, 3, -2, 1, 0, 1, 0, 0, 0, 2, 2, -3, -3, 2, 0, -1, 0, -1], 'schur_index': 1}
  • id: 7412392
    {'cdim': 8, 'counter': 32, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8i', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, -4, 4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, 0, 0, 0, 0, 1, -1, 2, 2, 2, 2, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412393
    {'cdim': 8, 'counter': 33, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8j', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 0, 0, 4, -4, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 3, -2, -2, 3, 0, 0, 0, 0, -1, 1, 2, 2, 2, 2, -3, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412394
    {'cdim': 8, 'counter': 34, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8k', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, 0, 0, 4, 4, 0, 0, 0, 0, -8, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 3, -2, -2, 3, -2, -1, 0, -1, 0, 0, 0, 2, 2, -3, -3, 2, 0, 1, 0, 1], 'schur_index': 1}
  • id: 7412395
    {'cdim': 8, 'counter': 35, 'faithful': False, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8l', 'multiplicity': 1, 'nt': [20, 154], 'qdim': 8, 'qvalues': [8, 8, 4, 4, 0, 0, 0, 0, 0, 0, -8, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -2, -2, 3, -2, -2, 0, -1, 0, -1, 0, 0, -3, -3, 2, 2, 2, 1, 0, 1, 0], 'schur_index': 1}
  • id: 7412396
    {'cdim': 8, 'counter': 36, 'faithful': True, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8m', 'multiplicity': 2, 'nt': [40, 1457], 'qdim': 16, 'qvalues': [16, -16, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, -4, -6, 4, 4, 0, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412397
    {'cdim': 8, 'counter': 37, 'faithful': True, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8n', 'multiplicity': 2, 'nt': [40, 1457], 'qdim': 16, 'qvalues': [16, -16, 0, 0, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 6, -4, 4, -6, 4, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412398
    {'cdim': 8, 'counter': 38, 'faithful': True, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8o', 'multiplicity': 2, 'nt': [40, 1457], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 6, -4, 4, -6, 4, 2, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412399
    {'cdim': 8, 'counter': 39, 'faithful': True, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.8p', 'multiplicity': 2, 'nt': [40, 1457], 'qdim': 16, 'qvalues': [16, -16, 8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, -4, -4, -6, 4, 4, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 7412401
    {'cdim': 16, 'counter': 40, 'faithful': True, 'group': '1600.9849', 'group_order': 1600, 'image': None, 'label': '1600.9849.16a', 'multiplicity': 1, 'nt': [40, 1437], 'qdim': 16, 'qvalues': [16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 6, 4, 4, -6, 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: 17186219
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 1600, 'label': '1600.9849.1a', '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]]]}
  • id: 17186230
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.h1', 'kernel_order': 800, 'label': '1600.9849.1b', '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]]]}
  • id: 17186241
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 3, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 800, 'label': '1600.9849.1c', '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]]]}
  • id: 17186252
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 4, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.f1', 'kernel_order': 800, 'label': '1600.9849.1d', '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]]]}
  • id: 17186260
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 5, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.g1', 'kernel_order': 800, 'label': '1600.9849.1e', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]]]}
  • id: 17186261
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 6, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 800, 'label': '1600.9849.1f', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]]]}
  • id: 17186262
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 7, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 800, 'label': '1600.9849.1g', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 17186263
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 8, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 800, 'label': '1600.9849.1h', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]]]}
  • id: 17186264
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 9, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 800, 'label': '1600.9849.1i', '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]]]}
  • id: 17186220
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 10, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.c1', 'kernel_order': 800, 'label': '1600.9849.1j', '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]]]}
  • id: 17186221
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 11, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 800, 'label': '1600.9849.1k', '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]]]}
  • id: 17186222
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 12, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 800, 'label': '1600.9849.1l', '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]]]}
  • id: 17186223
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 13, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.b1', 'kernel_order': 800, 'label': '1600.9849.1m', '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]]]}
  • id: 17186224
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 14, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.e1', 'kernel_order': 800, 'label': '1600.9849.1n', '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]]]}
  • id: 17186225
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 15, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 800, 'label': '1600.9849.1o', '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]]]}
  • id: 17186226
    {'center': '1.a1', 'center_index': 1, 'center_order': 1600, 'counter': 16, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.d1', 'kernel_order': 800, 'label': '1600.9849.1p', '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]]]}
  • id: 17186227
    {'center': '4.e1', 'center_index': 4, 'center_order': 400, 'counter': 17, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 200, 'label': '1600.9849.2a', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 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]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186228
    {'center': '4.e1', 'center_index': 4, 'center_order': 400, 'counter': 18, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 200, 'label': '1600.9849.2b', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 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]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186229
    {'center': '4.e1', 'center_index': 4, 'center_order': 400, 'counter': 19, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 200, 'label': '1600.9849.2c', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 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]], [[-2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186231
    {'center': '4.e1', 'center_index': 4, 'center_order': 400, 'counter': 20, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '8.3', 'image_order': 8, 'indicator': 1, 'kernel': '8.i1', 'kernel_order': 200, 'label': '1600.9849.2d', 'nt': [4, 3], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 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]], [[2, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186232
    {'center': '4.k1', 'center_index': 4, 'center_order': 400, 'counter': 21, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1', 'kernel_order': 100, 'label': '1600.9849.2e1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[2, 0]], [[-2, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186233
    {'center': '4.k1', 'center_index': 4, 'center_order': 400, 'counter': 22, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.c1', 'kernel_order': 100, 'label': '1600.9849.2e2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 0]], [[2, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186234
    {'center': '4.k1', 'center_index': 4, 'center_order': 400, 'counter': 23, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 100, 'label': '1600.9849.2f1', 'nt': [8, 11], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[-2, 0]], [[2, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186235
    {'center': '4.k1', 'center_index': 4, 'center_order': 400, 'counter': 24, 'cyclotomic_n': 4, 'dim': 2, 'faithful': False, 'field': [1, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '16.13', 'image_order': 16, 'indicator': 0, 'kernel': '16.b1', 'kernel_order': 100, 'label': '1600.9849.2f2', 'nt': [8, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[2, 1]], [[-2, 1]], [[-2, 0]], [[-2, 1]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186236
    {'center': '16.a1', 'center_index': 16, 'center_order': 100, 'counter': 25, 'cyclotomic_n': 1, 'dim': 4, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '32.50', 'image_order': 32, 'indicator': -1, 'kernel': '32.c1', 'kernel_order': 50, 'label': '1600.9849.4a', 'nt': [16, 20], 'q_character': None, 'values': [[[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]]]}
  • id: 17186237
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 26, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8a', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186238
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 27, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8b', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 17186239
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 28, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8c', 'nt': [10, 27], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 17186240
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 29, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8d', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 17186242
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 30, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8e', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[8, 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]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[3, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 17186243
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 31, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '400.207', 'image_order': 400, 'indicator': 1, 'kernel': '400.a1', 'kernel_order': 4, 'label': '1600.9849.8f', 'nt': [20, 90], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[1, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186244
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 32, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8g', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]]]}
  • id: 17186245
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 33, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8h', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 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]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]]]}
  • id: 17186246
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 34, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8i', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 0]], [[4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186247
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 35, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8j', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[-4, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 17186248
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 36, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8k', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[0, 0]], [[0, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-8, 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]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[1, 0]]]}
  • id: 17186249
    {'center': '400.a1', 'center_index': 400, 'center_order': 4, 'counter': 37, 'cyclotomic_n': 1, 'dim': 8, 'faithful': False, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '800.1194', 'image_order': 800, 'indicator': 1, 'kernel': '800.a1', 'kernel_order': 2, 'label': '1600.9849.8l', 'nt': [20, 154], 'q_character': None, 'values': [[[8, 0]], [[8, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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]], [[0, 0]], [[0, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-3, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[0, 0]]]}
  • id: 17186250
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 38, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8m1', 'nt': [40, 1457], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-4, 3], [2, 5], [-4, 7]], [[4, 3], [-2, 5], [4, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]]]}
  • id: 17186251
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 39, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8m2', 'nt': [40, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[4, 3], [-2, 5], [4, 7]], [[-4, 3], [2, 5], [-4, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]]]}
  • id: 17186253
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 40, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8n1', 'nt': [40, 1457], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [2, 5], [-4, 7]], [[4, 3], [-2, 5], [4, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]]]}
  • id: 17186254
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 41, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8n2', 'nt': [40, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 3], [-2, 5], [4, 7]], [[-4, 3], [2, 5], [-4, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]]]}
  • id: 17186255
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 42, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8o1', 'nt': [40, 1457], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-4, 3], [2, 5], [-4, 7]], [[4, 3], [-2, 5], [4, 7]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]]]}
  • id: 17186256
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 43, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8o2', 'nt': [40, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[3, 0]], [[-2, 0]], [[2, 0]], [[-3, 0]], [[2, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[4, 3], [-2, 5], [4, 7]], [[-4, 3], [2, 5], [-4, 7]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]]]}
  • id: 17186257
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 44, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8p1', 'nt': [40, 1457], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[2, 3], [-1, 5], [2, 7]], [[-4, 3], [2, 5], [-4, 7]], [[4, 3], [-2, 5], [4, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]]]}
  • id: 17186258
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 45, 'cyclotomic_n': 20, 'dim': 8, 'faithful': True, 'field': [5, 0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 0, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.8p2', 'nt': [40, 2], 'q_character': None, 'values': [[[8, 0]], [[-8, 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]], [[3, 0]], [[-2, 0]], [[-2, 0]], [[-3, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[-2, 3], [1, 5], [-2, 7]], [[4, 3], [-2, 5], [4, 7]], [[-4, 3], [2, 5], [-4, 7]], [[0, 0]], [[2, 3], [-1, 5], [2, 7]], [[0, 0]], [[-2, 3], [1, 5], [-2, 7]], [[0, 0]]]}
  • id: 17186259
    {'center': '800.a1', 'center_index': 800, 'center_order': 2, 'counter': 46, 'cyclotomic_n': 1, 'dim': 16, 'faithful': True, 'field': [0, 1], 'group': '1600.9849', 'group_counter': 9849, 'group_order': 1600, 'image': None, 'image_isoclass': '1600.9849', 'image_order': 1600, 'indicator': 1, 'kernel': '1600.a1', 'kernel_order': 1, 'label': '1600.9849.16a', 'nt': [40, 1437], 'q_character': None, 'values': [[[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]], [[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]], [[6, 0]], [[4, 0]], [[4, 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]]]}
• 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: 79546409
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 1600, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 10, 'label': '1600.9849.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1600.9849', 'subgroup_hash': 9849, 'subgroup_order': 1600, 'subgroup_tex': 'D_5\\wr C_2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546511
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.970', 'subgroup_hash': 970, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2.D_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546522
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1047', 'subgroup_hash': 1047, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2:D_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546533
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1023', 'subgroup_hash': 1023, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546544
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1194', 'subgroup_hash': 1194, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2.C_2^3', 'supersolvable': False, 'sylow': 0}
  • id: 79546555
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 800, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1046', 'subgroup_hash': 1046, 'subgroup_order': 800, 'subgroup_tex': 'C_4\\times D_5\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 79546566
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 800, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.f1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.969', 'subgroup_hash': 969, 'subgroup_order': 800, 'subgroup_tex': 'D_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 79546577
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 800, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.g1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1024', 'subgroup_hash': 1024, 'subgroup_order': 800, 'subgroup_tex': 'D_{20}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546588
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 800, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.2.h1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '800.1062', 'subgroup_hash': 1062, 'subgroup_order': 800, 'subgroup_tex': '(C_5\\times C_{20}):Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 79546410
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.211', 'subgroup_hash': 211, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 79546421
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 400, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.169', 'subgroup_hash': 169, 'subgroup_order': 400, 'subgroup_tex': 'C_4\\times D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546432
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 400, 'counter': 12, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.129', 'subgroup_hash': 129, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546443
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.210', 'subgroup_hash': 210, 'subgroup_order': 400, 'subgroup_tex': 'D_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546454
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.211', 'subgroup_hash': 211, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 79546465
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.129', 'subgroup_hash': 129, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2:C_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546476
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.210', 'subgroup_hash': 210, 'subgroup_order': 400, 'subgroup_tex': 'D_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546487
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.125', 'subgroup_hash': 125, 'subgroup_order': 400, 'subgroup_tex': 'D_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546498
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 400, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.171', 'subgroup_hash': 171, 'subgroup_order': 400, 'subgroup_tex': 'C_{20}:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546509
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.158', 'subgroup_hash': 158, 'subgroup_order': 400, 'subgroup_tex': 'C_{20}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546512
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 400, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.152', 'subgroup_hash': 152, 'subgroup_order': 400, 'subgroup_tex': 'C_{20}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546513
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.159', 'subgroup_hash': 159, 'subgroup_order': 400, 'subgroup_tex': 'C_{20}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546514
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.m1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.126', 'subgroup_hash': 126, 'subgroup_order': 400, 'subgroup_tex': 'C_{10}.(C_2\\times F_5)', 'supersolvable': True, 'sylow': 0}
  • id: 79546515
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 400, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.n1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.130', 'subgroup_hash': 130, 'subgroup_order': 400, 'subgroup_tex': '(C_5\\times C_{10}).D_4', 'supersolvable': False, 'sylow': 0}
  • id: 79546516
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.212', 'subgroup_hash': 212, 'subgroup_order': 400, 'subgroup_tex': 'C_2\\times C_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 79546517
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 400, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.4.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.p1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '400.134', 'subgroup_hash': 134, 'subgroup_order': 400, 'subgroup_tex': '(C_5\\times C_{10}).Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 79546518
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.4.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.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': 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': '400.207', 'subgroup_hash': 207, 'subgroup_order': 400, 'subgroup_tex': 'D_5^2.C_2^2', 'supersolvable': False, 'sylow': 0}
  • id: 79546519
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546520
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.49', 'subgroup_hash': 49, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546521
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 200, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.33', 'subgroup_hash': 33, 'subgroup_order': 200, 'subgroup_tex': 'C_{20}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546523
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.23', 'subgroup_hash': 23, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546524
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 200, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.48', 'subgroup_hash': 48, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546525
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.47', 'subgroup_hash': 47, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546526
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.g1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.48', 'subgroup_hash': 48, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546527
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 200, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.h1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '200.48', 'subgroup_hash': 48, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546528
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 200, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.8.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.43', 'subgroup_hash': 43, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 79546529
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 100, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '200.28', 'subgroup_hash': 28, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546530
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '200.22', 'subgroup_hash': 22, 'subgroup_order': 200, 'subgroup_tex': 'C_{10}.D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546531
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 100, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '200.29', 'subgroup_hash': 29, 'subgroup_order': 200, 'subgroup_tex': 'C_5\\times D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546532
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '200.24', 'subgroup_hash': 24, 'subgroup_order': 200, 'subgroup_tex': 'D_{10}:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546534
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '200.43', 'subgroup_hash': 43, 'subgroup_order': 200, 'subgroup_tex': 'D_5\\wr C_2', 'supersolvable': False, 'sylow': 0}
  • id: 79546535
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546536
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '200.42', 'subgroup_hash': 42, 'subgroup_order': 200, 'subgroup_tex': 'D_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546537
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 100, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.8.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.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': 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': '200.44', 'subgroup_hash': 44, 'subgroup_order': 200, 'subgroup_tex': 'C_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
  • id: 79546538
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.10.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.204', 'subgroup_hash': 204, 'subgroup_order': 160, 'subgroup_tex': 'D_{10}.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546539
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.10.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '10.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': 10, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '160.207', 'subgroup_hash': 207, 'subgroup_order': 160, 'subgroup_tex': 'D_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546540
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 100, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.15', 'subgroup_hash': 15, 'subgroup_order': 100, 'subgroup_tex': 'C_5:D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546541
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 100, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.8', 'subgroup_hash': 8, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546542
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 100, 'counter': 48, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.13', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '100.7', 'subgroup_hash': 7, 'subgroup_order': 100, 'subgroup_tex': 'C_5^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546543
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 49, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.16.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546545
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 100, 'counter': 50, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.11', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546546
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 50, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546547
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 50, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, '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': '100.14', 'subgroup_hash': 14, 'subgroup_order': 100, 'subgroup_tex': 'C_5\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546548
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 50, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '100.6', 'subgroup_hash': 6, 'subgroup_order': 100, 'subgroup_tex': 'C_5:C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546549
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 50, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.i1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546550
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.j1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546551
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.k1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '100.13', 'subgroup_hash': 13, 'subgroup_order': 100, 'subgroup_tex': 'D_5^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546552
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '100.11', 'subgroup_hash': 11, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546553
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 50, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546554
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 50, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.16.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.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': 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': '100.12', 'subgroup_hash': 12, 'subgroup_order': 100, 'subgroup_tex': 'C_5:F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546556
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.36', 'subgroup_hash': 36, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546557
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546558
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.50', 'subgroup_hash': 50, 'subgroup_order': 80, 'subgroup_tex': 'C_2^2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546559
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.34', 'subgroup_hash': 34, 'subgroup_order': 80, 'subgroup_tex': 'D_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546560
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.39', 'subgroup_hash': 39, 'subgroup_order': 80, 'subgroup_tex': 'D_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546561
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.30', 'subgroup_hash': 30, 'subgroup_order': 80, 'subgroup_tex': 'C_4\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546562
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546563
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546564
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546565
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.20.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '20.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': 20, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.31', 'subgroup_hash': 31, 'subgroup_order': 80, 'subgroup_tex': 'C_{20}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546567
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '1600.9849.25.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '25.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': 25, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.228', 'subgroup_hash': 228, 'subgroup_order': 64, 'subgroup_tex': 'D_4:D_4', 'supersolvable': True, 'sylow': 2}
  • id: 79546568
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 50, 'counter': 71, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.5', 'subgroup_hash': 5, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546569
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 50, 'counter': 72, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.32.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.46', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 46, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546570
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 50, 'counter': 73, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1600.9849.32.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.50', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 50, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4.C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '50.4', 'subgroup_hash': 4, 'subgroup_order': 50, 'subgroup_tex': 'C_5:D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546571
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 25, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.32.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546572
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 25, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.32.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, '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': '50.3', 'subgroup_hash': 3, 'subgroup_order': 50, 'subgroup_tex': 'C_5\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546573
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546574
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.7', 'subgroup_hash': 7, 'subgroup_order': 40, 'subgroup_tex': 'C_{10}:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546575
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546576
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546578
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546579
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.10', 'subgroup_hash': 10, 'subgroup_order': 40, 'subgroup_tex': 'C_5\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546580
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.13', 'subgroup_hash': 13, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546581
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.8', 'subgroup_hash': 8, 'subgroup_order': 40, 'subgroup_tex': 'C_5:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546582
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 10, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.6', 'subgroup_hash': 6, 'subgroup_order': 40, 'subgroup_tex': 'D_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546583
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546584
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546585
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.5', 'subgroup_hash': 5, 'subgroup_order': 40, 'subgroup_tex': 'C_4\\times D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546586
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546587
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546589
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546590
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546591
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546592
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546593
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.40.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '40.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': 40, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.12', 'subgroup_hash': 12, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546594
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.30', 'subgroup_hash': 30, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546595
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.28', 'subgroup_hash': 28, 'subgroup_order': 32, 'subgroup_tex': 'C_4:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546596
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.23', 'subgroup_hash': 23, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2.D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546597
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546598
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546411
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.29', 'subgroup_hash': 29, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 79546412
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546413
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.50.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '50.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': 50, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.35', 'subgroup_hash': 35, 'subgroup_order': 32, 'subgroup_tex': 'C_4:Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 79546414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': True, 'core_order': 25, 'counter': 103, 'cyclic': False, 'direct': False, 'hall': 5, 'label': '1600.9849.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '64.228', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 228, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 64, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4:D_4', 'simple': False, 'solvable': True, 'special_labels': ['L2', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '25.2', 'subgroup_hash': 2, 'subgroup_order': 25, 'subgroup_tex': 'C_5^2', 'supersolvable': True, 'sylow': 5}
  • id: 79546415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546416
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546418
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546419
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546420
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 4, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.80.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546423
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 100, 'characteristic': False, 'core_order': 4, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.80.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546424
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.80.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
  • id: 79546425
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546426
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546427
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.1', 'subgroup_hash': 1, 'subgroup_order': 20, 'subgroup_tex': 'C_5:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546428
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546429
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546430
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546431
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.4', 'subgroup_hash': 4, 'subgroup_order': 20, 'subgroup_tex': 'D_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546433
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546434
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.r1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546435
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.s1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546436
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.t1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546437
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.80.u1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '80.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': 80, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.3', 'subgroup_hash': 3, 'subgroup_order': 20, 'subgroup_tex': 'F_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546438
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546439
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546440
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546441
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546442
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546444
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546445
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546446
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546447
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546448
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546449
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546450
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546451
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546452
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546453
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 79546455
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546456
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.100.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '100.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': 100, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546457
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.160.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546458
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.160.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546459
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 144, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.160.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546460
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 1, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546461
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.160.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
  • id: 79546462
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546463
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546464
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546466
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546467
    {'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.160.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '160.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': 160, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.1', 'subgroup_hash': 1, 'subgroup_order': 10, 'subgroup_tex': 'D_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546468
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546469
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546470
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 79546471
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 79546472
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 40, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546473
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546474
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546475
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546477
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546478
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546479
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546480
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546481
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546482
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546483
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546484
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.p1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546485
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.200.q1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '200.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': 200, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
  • id: 79546486
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 1, 'counter': 169, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.320.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546488
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 200, 'characteristic': False, 'core_order': 1, 'counter': 170, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.320.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '320.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': 320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 0}
  • id: 79546489
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 800, 'characteristic': True, 'core_order': 4, 'counter': 171, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.9849.400.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '400.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '400.207', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 207, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 400, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5^2.C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546490
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 2, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546491
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546492
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546493
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 2, 'counter': 175, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546494
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 176, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546495
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546496
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.h1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546497
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.i1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546499
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1600.9849.400.j1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
  • id: 79546500
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 181, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.k1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546501
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 182, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546502
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 183, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.m1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546503
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 184, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.400.n1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '400.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': 400, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
  • id: 79546504
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 2, 'counter': 185, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1600.9849.800.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '800.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '800.1194', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1194, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 800, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5^2.C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U1'], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546505
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 160, 'characteristic': False, 'core_order': 1, 'counter': 186, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.800.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546506
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 80, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.800.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546507
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.800.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546508
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '1600.9849.800.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '800.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': 800, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
  • id: 79546510
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1600.9849', 'ambient_counter': 9849, 'ambient_order': 1600, 'ambient_tex': 'D_5\\wr C_2:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 1600, 'characteristic': True, 'core_order': 1, 'counter': 190, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1600.9849.1600.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1600.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '1600.9849', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 9849, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1600, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'D_5\\wr C_2:D_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D3', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
• gps_subgroup_data •

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

  
  
  • id: 79546440
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.c1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1600, 'centralizer': '200.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.c1', '50.a1', '50.e1'], 'contains': ['200.c1', '200.h1', '200.l1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3587, -1, 3856, -1], 'generators': [401, 40], 'label': '1600.9849.100.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546409
    {'ambient': '1600.9849', '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': '800.a1', 'complements': ['1600.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '2.h1', '25.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5163, 5168, 4920, 5205], 'generators': [1, 4, 336, 40, 800, 320, 2, 400], 'label': '1600.9849.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '2.e1', '2.f1', '2.g1', '2.h1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546410
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.b1', '2.d1'], 'contains': ['8.a1', '8.b1', '8.g1', '8.n1', '100.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3928, 4135, 4243, 4165], 'generators': [3, 320, 800, 4, 40, 656], 'label': '1600.9849.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.d1'], 'normal_contains': ['8.a1', '8.b1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546411
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '50.f1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '64.202', 'aut_weyl_index': 400, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.f1', '25.a1'], 'contains': ['100.f1', '100.g1', '100.m1', '100.n1', '100.o1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [6251, -1, 5675, -1], 'generators': [401, 674, 440], 'label': '1600.9849.50.f1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546412
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '50.g1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '32.46', 'aut_weyl_index': 800, 'centralizer': '200.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1', '25.a1'], 'contains': ['100.g1', '100.h1', '100.i1', '100.j1', '100.k1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8311, -1, 7103, -1], 'generators': [41, 674, 400], 'label': '1600.9849.50.g1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546413
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '50.h1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '128.2216', 'aut_weyl_index': 200, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.h1', '25.a1'], 'contains': ['100.j1', '100.l1', '100.o1', '100.p1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6603, -1, 5897, -1], 'generators': [3, 682, 400], 'label': '1600.9849.50.h1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.h1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546414
    {'ambient': '1600.9849', 'aut_centralizer_order': 800, 'aut_label': '64.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 800, 'centralizer': '16.b1', 'complements': ['25.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '32.b1', '32.c1', '32.d1', '32.e1'], 'contains': ['320.a1', '320.b1'], 'core': '64.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5917, 5017, 6166, 5138], 'generators': [336, 320], 'label': '1600.9849.64.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': ['32.a1', '32.b1', '32.c1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '64.a1', 'projective_image': '1600.9849', 'quotient_action_image': '16.13', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 79546415
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.2', 'aut_weyl_index': 3200, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '40.a1', '40.b1', '40.e1'], 'contains': ['160.a1', '160.c1', '400.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [229, -1, 1830, -1], 'generators': [1, 336, 800], 'label': '1600.9849.80.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546416
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '40.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.f1', '40.c1', '40.d1', '40.e1'], 'contains': ['160.a1', '160.d1', '400.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [427, -1, 1416, -1], 'generators': [1, 1296, 800], 'label': '1600.9849.80.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '80.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546417
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.2', 'aut_weyl_index': 3200, 'centralizer': '80.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '40.f1', '40.g1', '40.h1'], 'contains': ['160.b1', '160.e1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8193, -1, 8790, -1], 'generators': [1307, 656, 800], 'label': '1600.9849.80.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '80.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.c1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 79546418
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '80.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '40.g1', '40.h1', '40.i1'], 'contains': ['160.b1', '160.f1', '400.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8701, -1, 9130, -1], 'generators': [1035, 976, 800], 'label': '1600.9849.80.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '80.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.d1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546419
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '80.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.a1', '40.e1', '40.j1', '40.l1', '40.n1', '40.p1'], 'contains': ['160.a1', '160.g1', '160.i1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2096, -1, 2899, -1], 'generators': [1012, 336, 800], 'label': '1600.9849.80.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546420
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '80.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '40.g1', '40.k1', '40.m1', '40.o1', '40.q1'], 'contains': ['160.b1', '160.h1', '160.j1', '400.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9294, -1, 7556, -1], 'generators': [1012, 656, 800], 'label': '1600.9849.80.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '80.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546421
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '4.b1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1', '2.e1'], 'contains': ['8.a1', '8.c1', '8.d1', '8.j1', '8.k1', '20.a1'], 'core': '4.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [2598, 5557, 2271, 5598], 'generators': [1, 320, 1012, 800, 400, 336], 'label': '1600.9849.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.b1', '2.c1', '2.e1'], 'normal_contains': ['8.a1', '8.c1', '8.d1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546422
    {'ambient': '1600.9849', 'aut_centralizer_order': 800, 'aut_label': '80.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '8.2', 'aut_weyl_index': 3200, 'centralizer': '8.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.b1', '40.a1', '40.c1', '40.j1'], 'contains': ['160.a1', '400.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [918, -1, 2173, -1], 'generators': [400, 800, 336], 'label': '1600.9849.80.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '80.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.g1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546423
    {'ambient': '1600.9849', 'aut_centralizer_order': 1600, 'aut_label': '80.h1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '8.2', 'aut_weyl_index': 3200, 'centralizer': '16.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1', '40.f1', '40.i1', '40.k1'], 'contains': ['160.b1', '400.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7435, -1, 8210, -1], 'generators': [400, 800, 656], 'label': '1600.9849.80.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '80.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.h1', 'subgroup_fusion': None, 'weyl_group': '8.2'}
  • id: 79546424
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '8.2', 'aut_weyl_index': 3200, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.h1', '40.a1', '40.d1', '40.l1'], 'contains': ['160.a1', '400.e1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [660, -1, 1131, -1], 'generators': [401, 800, 336], 'label': '1600.9849.80.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.i1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546425
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '80.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '40.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.h1', '40.b1', '40.c1', '40.l1'], 'contains': ['160.a1', '400.e1'], 'core': '800.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1080, -1, 1273, -1], 'generators': [401, 1296, 800], 'label': '1600.9849.80.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '80.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546426
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.k1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.c1', '40.b1', '40.d1', '40.j1'], 'contains': ['160.a1', '400.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1329, -1, 2031, -1], 'generators': [1412, 336, 800], 'label': '1600.9849.80.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.k1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.k1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546427
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '80.l1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1', '40.h1', '40.k1'], 'contains': ['160.b1', '400.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7697, -1, 7700, -1], 'generators': [1412, 656, 800], 'label': '1600.9849.80.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '80.l1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.l1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546428
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.m1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '40.e1', '40.r1'], 'contains': ['160.c1', '160.d1', '160.g1', '400.g1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2280, -1, 2726, -1], 'generators': [1, 336, 1012], 'label': '1600.9849.80.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.m1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.m1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546429
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.n1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.i1', '40.e1'], 'contains': ['160.c1', '160.d1', '160.i1', '400.h1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1560, -1, 2370, -1], 'generators': [1, 336, 212], 'label': '1600.9849.80.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '80.n1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.n1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546430
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.o1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.j1', '40.g1', '40.s1'], 'contains': ['160.e1', '160.f1', '160.h1', '400.i1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7172, -1, 7843, -1], 'generators': [1307, 656, 340], 'label': '1600.9849.80.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '80.o1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.o1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546431
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.p1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.k1', '40.g1'], 'contains': ['160.e1', '160.f1', '160.j1', '400.j1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [9083, -1, 8565, -1], 'generators': [1307, 656, 1140], 'label': '1600.9849.80.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '80.p1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.p1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546432
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.e1'], 'contains': ['8.a1', '8.d1', '8.h1', '100.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [3394, 2322, 3413, 2340], 'generators': [401, 320, 1012, 800, 40, 336], 'label': '1600.9849.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.e1'], 'normal_contains': ['8.a1', '8.d1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546433
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '80.q1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.e1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.e1', '40.m1', '40.s1'], 'contains': ['160.h1', '400.k1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [6863, -1, 7429, -1], 'generators': [41, 656, 1012], 'label': '1600.9849.80.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '80.q1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.q1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546434
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '80.r1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.l1', '40.n1', '40.r1'], 'contains': ['160.g1', '400.l1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [3500, -1, 3780, -1], 'generators': [2, 336, 4], 'label': '1600.9849.80.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1', 'old_label': '80.r1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.r1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546435
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '80.s1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.l1', '40.o1', '40.s1'], 'contains': ['160.h1', '400.l1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [6749, -1, 7315, -1], 'generators': [2, 656, 4], 'label': '1600.9849.80.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '80.s1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.s1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546436
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '80.t1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.m1', '40.p1', '40.r1'], 'contains': ['160.g1', '400.m1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 80, 'diagramx': [2881, -1, 3428, -1], 'generators': [3, 336, 4], 'label': '1600.9849.80.t1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1', 'old_label': '80.t1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.t1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546437
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '80.u1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.n1', '40.q1'], 'contains': ['160.j1', '400.n1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9871, -1, 7970, -1], 'generators': [441, 656, 212], 'label': '1600.9849.80.u1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.f1', 'old_label': '80.u1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '80.u1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546438
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '100.a1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1600, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '50.a1', '50.b1', '50.d1'], 'contains': ['200.c1', '200.d1', '200.k1', '200.m1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4669, -1, 4736, -1], 'generators': [3, 680, 800], 'label': '1600.9849.100.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546439
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '100.b1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.a1', '50.b1', '50.c1', '50.e1'], 'contains': ['200.a1', '200.b1', '200.c1', '200.g1', '200.h1'], 'core': '400.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3095, -1, 3223, -1], 'generators': [1, 400, 1012], 'label': '1600.9849.100.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546441
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.d1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '100.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.b1', '50.a1', '50.c1', '50.d1'], 'contains': ['200.c1', '200.j1', '200.k1', '200.n1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4901, -1, 4068, -1], 'generators': [1, 2, 800], 'label': '1600.9849.100.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546442
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.e1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '32.27', 'aut_weyl_index': 800, 'centralizer': '100.k1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '50.d1', '50.e1'], 'contains': ['200.c1', '200.i1', '200.o1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3328, -1, 3659, -1], 'generators': [1, 40, 800], 'label': '1600.9849.100.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546443
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1', '2.d1'], 'contains': ['8.a1', '8.f1', '8.g1', '8.o1', '20.b1'], 'core': '4.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [3615, 4915, 2833, 4951], 'generators': [1, 320, 800, 4, 2, 336], 'label': '1600.9849.4.d1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.a1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546444
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '100.f1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '16.14', 'aut_weyl_index': 1600, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.f1', '50.a1', '50.b1', '50.f1'], 'contains': ['200.d1', '200.h1', '200.k1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5337, -1, 5079, -1], 'generators': [401, 682], 'label': '1600.9849.100.f1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.f1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546445
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '100.g1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '100.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.c1', '50.d1', '50.f1', '50.g1'], 'contains': ['200.d1', '200.i1', '200.j1', '200.p1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [6881, -1, 7018, -1], 'generators': [41, 674, 800], 'label': '1600.9849.100.g1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.g1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546446
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '100.h1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '200.i1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.d1', '50.a1', '50.g1'], 'contains': ['200.d1', '200.j1', '200.l1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [8704, -1, 7361, -1], 'generators': [441, 674], 'label': '1600.9849.100.h1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.h1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546447
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '100.i1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1600, 'centralizer': '200.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.e1', '50.b1', '50.g1'], 'contains': ['200.d1', '200.e1', '200.f1', '200.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [8205, -1, 8339, -1], 'generators': [683, 400, 372], 'label': '1600.9849.100.i1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.i1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546448
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '100.j1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '100.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.f1', '50.e1', '50.g1', '50.h1'], 'contains': ['200.g1', '200.i1', '200.l1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7791, -1, 6829, -1], 'generators': [41, 400], 'label': '1600.9849.100.j1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.j1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546449
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '100.k1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '100.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.g1', '20.h1', '50.c1', '50.g1'], 'contains': ['200.g1', '200.j1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5751, -1, 6692, -1], 'generators': [2, 400], 'label': '1600.9849.100.k1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.k1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546450
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.l1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '16.11', 'aut_weyl_index': 1600, 'centralizer': '200.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['20.i1', '50.b1', '50.c1', '50.h1'], 'contains': ['200.g1', '200.k1'], 'core': '400.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4488, -1, 4917, -1], 'generators': [3, 400], 'label': '1600.9849.100.l1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.l1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.l1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546451
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.m1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '8.5', 'aut_weyl_index': 3200, 'centralizer': '200.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['20.j1', '50.a1', '50.c1', '50.f1'], 'contains': ['200.h1', '200.j1', '200.k1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5098, -1, 4410, -1], 'generators': [401, 2], 'label': '1600.9849.100.m1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.m1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.m1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546452
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '100.n1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '32.27', 'aut_weyl_index': 800, 'centralizer': '200.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.n1', '50.e1', '50.f1'], 'contains': ['200.h1', '200.i1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [4092, -1, 4555, -1], 'generators': [401, 440], 'label': '1600.9849.100.n1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.n1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.n1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.n1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546453
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '100.o1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '32.27', 'aut_weyl_index': 800, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.o1', '50.d1', '50.f1', '50.h1'], 'contains': ['200.i1', '200.k1', '200.q1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5933, -1, 5337, -1], 'generators': [3, 682, 800], 'label': '1600.9849.100.o1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.o1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.o1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546454
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '4.e1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '3200.ga', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '2.e1'], 'contains': ['8.a1', '8.e1', '8.i1', '100.e1'], 'core': '4.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [3124, 416, 3144, 419], 'generators': [1, 320, 800, 1012, 40, 336], 'label': '1600.9849.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.d1', '2.e1'], 'normal_contains': ['8.a1', '8.e1', '8.i1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546455
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '100.p1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '32.27', 'aut_weyl_index': 800, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.p1', '50.a1', '50.h1'], 'contains': ['200.k1', '200.l1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [6563, -1, 5518, -1], 'generators': [403, 682], 'label': '1600.9849.100.p1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.p1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '100.p1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.p1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546456
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '100.q1', 'aut_quo_index': None, 'aut_stab_index': 400, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.q1', '50.d1'], 'contains': ['200.m1', '200.n1', '200.o1', '200.p1', '200.q1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [3887, -1, 4265, -1], 'generators': [1, 674, 40], 'label': '1600.9849.100.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '100.q1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '100.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546457
    {'ambient': '1600.9849', 'aut_centralizer_order': 1600, 'aut_label': '160.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '8.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.a1', '80.a1', '80.b1', '80.e1', '80.g1', '80.i1', '80.j1', '80.k1'], 'contains': ['320.a1', '800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1060, -1, 2102, -1], 'generators': [800, 336], 'label': '1600.9849.160.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '160.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546458
    {'ambient': '1600.9849', 'aut_centralizer_order': 3200, 'aut_label': '160.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '8.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '80.c1', '80.d1', '80.f1', '80.h1', '80.l1'], 'contains': ['320.b1', '800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7552, -1, 7677, -1], 'generators': [800, 656], 'label': '1600.9849.160.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '160.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546459
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '160.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '80.a1', '80.m1', '80.n1'], 'contains': ['320.a1', '800.b1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1827, -1, 2700, -1], 'generators': [1, 336], 'label': '1600.9849.160.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.c1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.c1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546460
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '160.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '40.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['32.d1', '80.b1', '80.m1', '80.n1'], 'contains': ['320.a1', '800.b1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1568, -1, 2560, -1], 'generators': [1, 1296], 'label': '1600.9849.160.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '160.d1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546461
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '160.e1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '80.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.e1', '80.c1', '80.o1', '80.p1'], 'contains': ['320.b1', '800.c1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7374, -1, 7945, -1], 'generators': [1307, 656], 'label': '1600.9849.160.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '160.e1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.e1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546462
    {'ambient': '1600.9849', 'aut_centralizer_order': 160, 'aut_label': '160.f1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '80.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.e1', '80.d1', '80.o1', '80.p1'], 'contains': ['320.b1', '800.c1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8438, -1, 8071, -1], 'generators': [1035, 976], 'label': '1600.9849.160.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '160.f1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.f1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546463
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '160.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.b1', '80.e1', '80.m1', '80.r1', '80.t1'], 'contains': ['320.a1', '800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2554, -1, 3428, -1], 'generators': [1012, 336], 'label': '1600.9849.160.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.g1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.g1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546464
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '160.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1', '80.f1', '80.o1', '80.q1', '80.s1'], 'contains': ['320.b1', '800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [6639, -1, 7322, -1], 'generators': [1012, 656], 'label': '1600.9849.160.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '160.h1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.h1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546465
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.f1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.b1', '2.f1'], 'contains': ['8.b1', '8.d1', '8.g1', '100.f1'], 'core': '4.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [5163, 6751, 5036, 6801], 'generators': [401, 320, 548, 800, 362, 1296], 'label': '1600.9849.4.f1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.f1', 'normal_contained_in': ['2.a1', '2.b1', '2.f1'], 'normal_contains': ['8.b1', '8.d1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546466
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '160.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['32.c1', '80.e1', '80.n1'], 'contains': ['320.a1', '800.e1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1980, -1, 3212, -1], 'generators': [212, 336], 'label': '1600.9849.160.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '160.i1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.i1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546467
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '160.j1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '200.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1', '80.f1', '80.p1', '80.u1'], 'contains': ['320.b1', '800.e1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9183, -1, 7552, -1], 'generators': [212, 656], 'label': '1600.9849.160.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '160.j1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '160.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546468
    {'ambient': '1600.9849', 'aut_centralizer_order': 320, 'aut_label': '200.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '20.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.a1', '40.c1', '100.b1'], 'contains': ['400.a1', '400.b1', '400.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [980, -1, 1594, -1], 'generators': [1, 400], 'label': '1600.9849.200.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '200.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546469
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '200.b1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.b1', '40.d1', '100.b1'], 'contains': ['400.b1', '400.e1', '400.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [1315, -1, 955, -1], 'generators': [1, 1412], 'label': '1600.9849.200.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.c1', 'old_label': '200.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546470
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '200.c1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '50.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.e1', '100.a1', '100.b1', '100.c1', '100.d1', '100.e1'], 'contains': ['400.b1', '400.d1', '400.g1', '400.h1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3328, -1, 3659, -1], 'generators': [1, 1012, 800], 'label': '1600.9849.200.c1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546471
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '200.d1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '100.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.g1', '100.a1', '100.f1', '100.g1', '100.h1', '100.i1'], 'contains': ['400.c1', '400.d1', '400.i1', '400.j1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [7647, -1, 7194, -1], 'generators': [683, 372, 800], 'label': '1600.9849.200.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546472
    {'ambient': '1600.9849', 'aut_centralizer_order': 320, 'aut_label': '200.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '40.m1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.f1', '40.i1', '100.i1'], 'contains': ['400.a1', '400.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7155, -1, 8976, -1], 'generators': [683, 400], 'label': '1600.9849.200.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '200.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.e1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546473
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '200.f1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '200.i1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.h1', '100.i1'], 'contains': ['400.c1', '400.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [8206, -1, 8084, -1], 'generators': [683, 772], 'label': '1600.9849.200.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.g1', 'old_label': '200.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546474
    {'ambient': '1600.9849', 'aut_centralizer_order': 512, 'aut_label': '200.g1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.j1', '40.k1', '100.b1', '100.i1', '100.j1', '100.k1', '100.l1'], 'contains': ['400.a1', '400.d1', '400.f1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5573, -1, 6022, -1], 'generators': [400, 1012], 'label': '1600.9849.200.g1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546475
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '200.h1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '100.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.l1', '100.b1', '100.c1', '100.f1', '100.m1', '100.n1'], 'contains': ['400.d1', '400.e1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [3575, -1, 4405, -1], 'generators': [401, 1012], 'label': '1600.9849.200.h1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.h1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546476
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.g1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '3200.ih', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.f1', '2.g1'], 'contains': ['8.b1', '8.e1', '8.f1', '8.p1', '20.c1'], 'core': '4.g1', 'coset_action_label': None, 'count': 2, 'diagramx': [6181, 6199, 6816, 6245], 'generators': [41, 320, 800, 1012, 2, 336], 'label': '1600.9849.4.g1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.g1', 'normal_contained_in': ['2.d1', '2.f1', '2.g1'], 'normal_contains': ['8.b1', '8.e1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.g1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546477
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '200.i1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '50.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.m1', '100.e1', '100.g1', '100.j1', '100.n1', '100.o1'], 'contains': ['400.d1', '400.k1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6337, -1, 6450, -1], 'generators': [41, 800], 'label': '1600.9849.200.i1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546478
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '200.j1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['40.n1', '40.o1', '100.d1', '100.g1', '100.h1', '100.k1', '100.m1'], 'contains': ['400.d1', '400.l1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5787, -1, 6236, -1], 'generators': [2, 800], 'label': '1600.9849.200.j1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546479
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '200.k1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '100.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.p1', '100.a1', '100.d1', '100.f1', '100.l1', '100.m1', '100.o1', '100.p1'], 'contains': ['400.d1', '400.m1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [4984, -1, 4827, -1], 'generators': [3, 800], 'label': '1600.9849.200.k1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.k1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.k1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546480
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '200.l1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '100.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.q1', '100.c1', '100.h1', '100.j1', '100.p1'], 'contains': ['400.d1', '400.n1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7837, -1, 6664, -1], 'generators': [441, 800], 'label': '1600.9849.200.l1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.l1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.l1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546481
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '200.m1', 'aut_quo_index': None, 'aut_stab_index': 400, 'aut_weyl_group': '4.2', 'aut_weyl_index': 6400, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.n1', '100.a1', '100.q1'], 'contains': ['400.g1', '400.i1', '400.m1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [3776, -1, 4621, -1], 'generators': [3, 680], 'label': '1600.9849.200.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '200.m1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.m1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546482
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '200.n1', 'aut_quo_index': None, 'aut_stab_index': 400, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.d1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['40.r1', '100.d1', '100.q1'], 'contains': ['400.g1', '400.l1', '400.m1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 400, 'diagramx': [4045, -1, 4074, -1], 'generators': [1, 2], 'label': '1600.9849.200.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '200.n1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546483
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '200.o1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '100.k1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.i1', '100.e1', '100.q1'], 'contains': ['400.g1', '400.k1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3181, -1, 4238, -1], 'generators': [1, 40], 'label': '1600.9849.200.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '200.o1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.o1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546484
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '200.p1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['40.s1', '100.g1', '100.q1'], 'contains': ['400.i1', '400.k1', '400.l1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [6062, -1, 7023, -1], 'generators': [41, 674], 'label': '1600.9849.200.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '200.p1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.p1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546485
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '200.q1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '8.3', 'aut_weyl_index': 3200, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.q1', '100.o1', '100.q1'], 'contains': ['400.k1', '400.m1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [4247, -1, 5198, -1], 'generators': [3, 682], 'label': '1600.9849.200.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '200.q1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '200.q1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 79546486
    {'ambient': '1600.9849', 'aut_centralizer_order': 1600, 'aut_label': '320.a1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '8.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['64.a1', '160.a1', '160.c1', '160.d1', '160.g1', '160.i1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1950, -1, 3212, -1], 'generators': [336], 'label': '1600.9849.320.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '320.a1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546487
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.h1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '3200.ih', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.g1'], 'contains': ['8.b1', '8.f1', '8.h1', '20.d1'], 'core': '4.h1', 'coset_action_label': None, 'count': 2, 'diagramx': [7292, 7799, 7229, 7857], 'generators': [441, 320, 212, 800, 2, 336], 'label': '1600.9849.4.h1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.h1', 'normal_contained_in': ['2.a1', '2.g1'], 'normal_contains': ['8.b1', '8.f1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.h1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546488
    {'ambient': '1600.9849', 'aut_centralizer_order': 3200, 'aut_label': '320.b1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '4.1', 'aut_weyl_index': 6400, 'centralizer': '8.l1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '160.b1', '160.e1', '160.f1', '160.h1', '160.j1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7389, -1, 7552, -1], 'generators': [656], 'label': '1600.9849.320.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '64.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '320.b1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '320.b1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546489
    {'ambient': '1600.9849', 'aut_centralizer_order': 12800, 'aut_label': '400.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '2.e1', 'complements': ['4.q1'], 'conjugacy_class_count': 1, 'contained_in': ['80.g1', '80.h1', '200.a1', '200.e1', '200.g1'], 'contains': ['800.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5159, 9584, 5916, 9893], 'generators': [400], 'label': '1600.9849.400.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '400.a1', 'normal_contained_in': ['16.b1'], 'normal_contains': ['800.a1'], 'normalizer': '1.a1', 'old_label': '400.a1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '200.43', 'quotient_action_kernel_order': 200, 'quotient_fusion': None, 'short_label': '400.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546490
    {'ambient': '1600.9849', 'aut_centralizer_order': 640, 'aut_label': '400.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '10.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.a1', '80.b1', '200.a1', '200.b1', '200.c1'], 'contains': ['800.a1', '800.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [815, -1, 1830, -1], 'generators': [1, 800], 'label': '1600.9849.400.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '400.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546491
    {'ambient': '1600.9849', 'aut_centralizer_order': 640, 'aut_label': '400.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '20.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.c1', '80.d1', '200.d1', '200.e1', '200.f1'], 'contains': ['800.a1', '800.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7647, -1, 8192, -1], 'generators': [683, 800], 'label': '1600.9849.400.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '400.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546492
    {'ambient': '1600.9849', 'aut_centralizer_order': 1024, 'aut_label': '400.d1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.e1', '80.f1', '200.c1', '200.d1', '200.g1', '200.h1', '200.i1', '200.j1', '200.k1', '200.l1'], 'contains': ['800.a1', '800.d1', '800.e1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5968, -1, 6037, -1], 'generators': [1012, 800], 'label': '1600.9849.400.d1', 'mobius_quo': None, 'mobius_sub': -64, 'normal_closure': '16.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546493
    {'ambient': '1600.9849', 'aut_centralizer_order': 640, 'aut_label': '400.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '20.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.i1', '80.j1', '200.a1', '200.b1', '200.h1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1242, -1, 1433, -1], 'generators': [401], 'label': '1600.9849.400.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '400.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546494
    {'ambient': '1600.9849', 'aut_centralizer_order': 512, 'aut_label': '400.f1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.k1', '80.l1', '200.b1', '200.f1', '200.g1'], 'contains': ['800.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5308, -1, 5803, -1], 'generators': [1412], 'label': '1600.9849.400.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546495
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '400.g1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.m1', '200.c1', '200.m1', '200.n1', '200.o1'], 'contains': ['800.b1', '800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [3328, -1, 4074, -1], 'generators': [1, 1012], 'label': '1600.9849.400.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.g1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.g1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546496
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '400.h1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.n1', '200.c1'], 'contains': ['800.b1', '800.e1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [2044, -1, 2886, -1], 'generators': [1, 212], 'label': '1600.9849.400.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.c1', 'old_label': '400.h1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.h1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546497
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '400.i1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.o1', '200.d1', '200.m1', '200.p1'], 'contains': ['800.c1', '800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [6773, -1, 7116, -1], 'generators': [683, 372], 'label': '1600.9849.400.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '400.i1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.i1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546498
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.i1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6400.ex', 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.g1'], 'contains': ['8.b1', '8.c1', '8.l1', '8.m1', '20.e1'], 'core': '4.i1', 'coset_action_label': None, 'count': 1, 'diagramx': [6566, 8848, 8202, 8913], 'generators': [1307, 320, 1012, 800, 400, 976], 'label': '1600.9849.4.i1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.i1', 'normal_contained_in': ['2.b1', '2.g1'], 'normal_contains': ['8.b1', '8.c1'], 'normalizer': '1.a1', 'old_label': '4.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.i1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546499
    {'ambient': '1600.9849', 'aut_centralizer_order': 128, 'aut_label': '400.j1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.p1', '200.d1'], 'contains': ['800.c1', '800.e1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [7776, -1, 7811, -1], 'generators': [683, 1172], 'label': '1600.9849.400.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.f1', 'old_label': '400.j1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.j1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546500
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '400.k1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '50.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.q1', '200.i1', '200.o1', '200.p1', '200.q1'], 'contains': ['800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [5830, -1, 6418, -1], 'generators': [41], 'label': '1600.9849.400.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '400.k1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.k1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546501
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '400.l1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '50.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['80.r1', '80.s1', '200.j1', '200.n1', '200.p1'], 'contains': ['800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5699, -1, 6288, -1], 'generators': [2], 'label': '1600.9849.400.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '400.l1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.l1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546502
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '400.m1', 'aut_quo_index': None, 'aut_stab_index': 200, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['80.t1', '200.k1', '200.m1', '200.n1', '200.q1'], 'contains': ['800.d1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 200, 'diagramx': [4146, -1, 4723, -1], 'generators': [3], 'label': '1600.9849.400.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.d1', 'old_label': '400.m1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.m1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546503
    {'ambient': '1600.9849', 'aut_centralizer_order': 256, 'aut_label': '400.n1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '2.1', 'aut_weyl_index': 12800, 'centralizer': '100.j1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.u1', '200.l1'], 'contains': ['800.e1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [8856, -1, 7435, -1], 'generators': [441], 'label': '1600.9849.400.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '50.h1', 'old_label': '400.n1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '400.n1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 79546539
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 80, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.g1'], 'contains': ['20.c1', '20.d1', '20.e1', '20.f1', '20.h1', '50.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8462, -1, 7740, -1], 'generators': [41, 656, 400, 1012, 674, 800], 'label': '1600.9849.10.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '10.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.b1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546504
    {'ambient': '1600.9849', 'aut_centralizer_order': 25600, 'aut_label': '800.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['160.a1', '160.b1', '400.a1', '400.b1', '400.c1', '400.d1', '400.e1', '400.f1'], 'contains': ['1600.a1'], 'core': '800.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5308, 9584, 5916, 9893], 'generators': [800], 'label': '1600.9849.800.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '800.a1', 'normal_contained_in': ['32.a1', '400.a1'], 'normal_contains': ['1600.a1'], 'normalizer': '1.a1', 'old_label': '800.a1', 'projective_image': '800.1194', 'quotient_action_image': '1.1', 'quotient_action_kernel': '800.1194', 'quotient_action_kernel_order': 800, 'quotient_fusion': None, 'short_label': '800.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546505
    {'ambient': '1600.9849', 'aut_centralizer_order': 640, 'aut_label': '800.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '10.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['160.c1', '160.d1', '400.b1', '400.g1', '400.h1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [1817, -1, 2768, -1], 'generators': [1], 'label': '1600.9849.800.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '800.b1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546506
    {'ambient': '1600.9849', 'aut_centralizer_order': 640, 'aut_label': '800.c1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '20.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['160.e1', '160.f1', '400.c1', '400.i1', '400.j1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [7605, -1, 7877, -1], 'generators': [683], 'label': '1600.9849.800.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '800.c1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546507
    {'ambient': '1600.9849', 'aut_centralizer_order': 1024, 'aut_label': '800.d1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.g1', '160.h1', '400.d1', '400.g1', '400.i1', '400.k1', '400.l1', '400.m1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [5755, -1, 6037, -1], 'generators': [1012], 'label': '1600.9849.800.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '800.d1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546508
    {'ambient': '1600.9849', 'aut_centralizer_order': 1024, 'aut_label': '800.e1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '1.1', 'aut_weyl_index': 25600, 'centralizer': '25.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['160.i1', '160.j1', '400.d1', '400.h1', '400.j1', '400.n1'], 'contains': ['1600.a1'], 'core': '1600.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [7449, -1, 6151, -1], 'generators': [212], 'label': '1600.9849.800.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '800.e1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '800.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546509
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '4.j1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '3200.ih', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '2.g1', '2.h1'], 'contains': ['8.c1', '8.e1', '8.h1', '20.f1'], 'core': '4.j1', 'coset_action_label': None, 'count': 1, 'diagramx': [7040, 2874, 6554, 2895], 'generators': [41, 320, 1012, 800, 400, 336], 'label': '1600.9849.4.j1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.j1', 'normal_contained_in': ['2.e1', '2.g1', '2.h1'], 'normal_contains': ['8.c1', '8.e1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.j1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546510
    {'ambient': '1600.9849', 'aut_centralizer_order': None, 'aut_label': '1600.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['320.a1', '320.b1', '800.a1', '800.b1', '800.c1', '800.d1', '800.e1'], 'contains': [], 'core': '1600.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5755, 9584, 6037, 9893], 'generators': [], 'label': '1600.9849.1600.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1600.a1', 'normal_contained_in': ['64.a1', '800.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '1600.a1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1600.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 79546511
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '3200.jb', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': ['800.b1', '800.c1'], 'conjugacy_class_count': 4, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.c1', '4.d1', '4.f1', '4.h1', '4.m1', '4.p1', '50.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [5163, 5577, 4577, 5618], 'generators': [401, 336, 40, 4, 2, 320, 800], 'label': '1600.9849.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.c1', '4.d1', '4.f1', '4.h1', '4.m1', '4.p1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546512
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.k1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6400.ex', 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '2.g1'], 'contains': ['8.c1', '8.f1', '20.g1', '20.h1'], 'core': '4.k1', 'coset_action_label': None, 'count': 1, 'diagramx': [5837, 9375, 6207, 9444], 'generators': [2, 320, 4, 800, 400, 336], 'label': '1600.9849.4.k1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.k1', 'normal_contained_in': ['2.c1', '2.g1'], 'normal_contains': ['8.c1', '8.f1'], 'normalizer': '1.a1', 'old_label': '4.k1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.k1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546513
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.l1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '3200.et', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '2.c1', '2.h1'], 'contains': ['8.c1', '8.g1', '20.i1'], 'core': '4.l1', 'coset_action_label': None, 'count': 2, 'diagramx': [4701, 8363, 4528, 8424], 'generators': [3, 320, 4, 800, 400, 336], 'label': '1600.9849.4.l1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.l1', 'normal_contained_in': ['2.b1', '2.c1', '2.h1'], 'normal_contains': ['8.c1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.l1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.l1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546514
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.m1', 'aut_quo_index': 6, 'aut_stab_index': 4, 'aut_weyl_group': '1600.10264', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '2.c1', '2.f1'], 'contains': ['8.d1', '8.f1', '8.g1', '20.j1'], 'core': '4.m1', 'coset_action_label': None, 'count': 4, 'diagramx': [4909, 7236, 3667, 7289], 'generators': [401, 320, 4, 800, 2, 336], 'label': '1600.9849.4.m1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.m1', 'normal_contained_in': ['2.a1', '2.c1', '2.f1'], 'normal_contains': ['8.d1', '8.f1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.m1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.m1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546515
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '4.n1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '3200.ga', 'aut_weyl_index': 8, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '2.f1'], 'contains': ['8.d1', '8.e1', '100.n1'], 'core': '4.n1', 'coset_action_label': None, 'count': 1, 'diagramx': [4498, 1113, 4729, 1121], 'generators': [401, 320, 1012, 800, 440, 336], 'label': '1600.9849.4.n1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.n1', 'normal_contained_in': ['2.e1', '2.f1'], 'normal_contains': ['8.d1', '8.e1'], 'normalizer': '1.a1', 'old_label': '4.n1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.n1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546516
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.o1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '3200.ga', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '2.f1', '2.h1'], 'contains': ['8.e1', '8.g1', '8.q1', '100.o1'], 'core': '4.o1', 'coset_action_label': None, 'count': 2, 'diagramx': [5568, 1728, 5604, 1740], 'generators': [3, 320, 800, 4, 362, 336], 'label': '1600.9849.4.o1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.o1', 'normal_contained_in': ['2.d1', '2.f1', '2.h1'], 'normal_contains': ['8.e1', '8.g1'], 'normalizer': '1.a1', 'old_label': '4.o1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546517
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '4.p1', 'aut_quo_index': 3, 'aut_stab_index': 2, 'aut_weyl_group': '3200.ga', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.h1'], 'contains': ['8.g1', '8.h1', '100.p1'], 'core': '4.p1', 'coset_action_label': None, 'count': 2, 'diagramx': [6813, 3442, 5908, 3467], 'generators': [403, 320, 4, 800, 362, 336], 'label': '1600.9849.4.p1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.p1', 'normal_contained_in': ['2.a1', '2.h1'], 'normal_contains': ['8.g1', '8.h1'], 'normalizer': '1.a1', 'old_label': '4.p1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.p1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546518
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '4.q1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['2.d1'], 'contains': ['8.i1', '8.n1', '8.o1', '8.p1', '8.q1', '100.q1'], 'core': '8.i1', 'coset_action_label': None, 'count': 16, 'diagramx': [4255, -1, 3917, -1], 'generators': [1, 320, 40, 4, 2, 336], 'label': '1600.9849.4.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '4.q1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.q1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546519
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '8.a1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '800.1194', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'contains': ['16.a1', '16.d1', '16.f1', '16.i1', '40.e1'], 'core': '8.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2998, 3694, 1894, 3721], 'generators': [1, 800, 336, 1012, 320], 'label': '1600.9849.8.a1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1'], 'normal_contains': ['16.a1', '16.d1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546520
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'contains': ['16.a1', '16.g1', '16.j1', '16.k1', '40.g1'], 'core': '8.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [7030, 6199, 8202, 6245], 'generators': [1307, 800, 976, 1012, 320], 'label': '1600.9849.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.f1', '4.g1', '4.h1', '4.i1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546559
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '20.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.h1', '10.b1'], 'contains': ['40.g1', '40.o1', '40.q1', '100.h1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [9732, -1, 8414, -1], 'generators': [441, 212, 800, 674, 656], 'label': '1600.9849.20.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '20.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.d1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546521
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '8.c1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1', '4.i1', '4.j1', '4.k1', '4.l1'], 'contains': ['16.a1', '16.b1', '16.c1', '40.j1', '40.k1'], 'core': '8.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5553, 7582, 6160, 7638], 'generators': [400, 800, 336, 1012, 320], 'label': '1600.9849.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.i1', '4.j1', '4.k1', '4.l1'], 'normal_contains': ['16.a1', '16.b1', '16.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546522
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': ['800.b1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.f1', '4.i1', '4.l1', '50.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [4409, 6436, 4920, 6484], 'generators': [3, 656, 400, 4, 40, 320, 800], 'label': '1600.9849.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.f1', '4.i1', '4.l1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546523
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '8.d1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '800.1194', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '4.c1', '4.f1', '4.m1', '4.n1'], 'contains': ['16.a1', '16.h1', '40.l1'], 'core': '8.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [3661, 4293, 3317, 4324], 'generators': [401, 800, 336, 1012, 320], 'label': '1600.9849.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.b1', '4.c1', '4.f1', '4.m1', '4.n1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546524
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '8.e1', 'aut_quo_index': 84, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.e1', '4.g1', '4.j1', '4.n1', '4.o1'], 'contains': ['16.a1', '16.e1', '40.m1'], 'core': '8.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [6266, 2874, 6864, 2895], 'generators': [41, 1012, 336, 800, 320], 'label': '1600.9849.8.e1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.e1', 'normal_contained_in': ['4.e1', '4.g1', '4.j1', '4.n1', '4.o1'], 'normal_contains': ['16.a1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546525
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '8.f1', 'aut_quo_index': 84, 'aut_stab_index': 2, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.d1', '4.g1', '4.h1', '4.k1', '4.m1'], 'contains': ['16.a1', '16.l1', '40.n1', '40.o1'], 'core': '8.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [5837, 6881, 6440, 6932], 'generators': [2, 4, 336, 800, 320], 'label': '1600.9849.8.f1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.f1', 'normal_contained_in': ['4.d1', '4.g1', '4.h1', '4.k1', '4.m1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546526
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '8.g1', 'aut_quo_index': 168, 'aut_stab_index': 4, 'aut_weyl_group': '800.1194', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.d1', '4.f1', '4.l1', '4.m1', '4.o1', '4.p1'], 'contains': ['16.a1', '16.m1', '40.p1'], 'core': '8.g1', 'coset_action_label': None, 'count': 4, 'diagramx': [4568, 5561, 4403, 5602], 'generators': [3, 4, 336, 800, 320], 'label': '1600.9849.8.g1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.g1', 'normal_contained_in': ['4.a1', '4.d1', '4.f1', '4.l1', '4.m1', '4.o1', '4.p1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.g1', 'projective_image': '800.1194', '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': '800.1194'}
  • id: 79546527
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '8.h1', 'aut_quo_index': 42, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.h1', '4.j1', '4.p1'], 'contains': ['16.a1', '16.n1', '40.q1'], 'core': '8.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [8071, 4908, 7342, 4944], 'generators': [441, 212, 336, 800, 320], 'label': '1600.9849.8.h1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.h1', 'normal_contained_in': ['4.c1', '4.h1', '4.j1', '4.p1'], 'normal_contains': ['16.a1'], 'normalizer': '1.a1', 'old_label': '8.h1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546528
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '8.i1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': ['200.e1', '200.f1'], 'conjugacy_class_count': 4, 'contained_in': ['4.e1', '4.q1'], 'contains': ['16.d1', '16.e1', '200.o1'], 'core': '8.i1', 'coset_action_label': None, 'count': 4, 'diagramx': [3424, 2244, 2962, 2260], 'generators': [1, 1012, 336, 40, 320], 'label': '1600.9849.8.i1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.i1', 'normal_contained_in': ['4.e1'], 'normal_contains': ['16.d1', '16.e1'], 'normalizer': '1.a1', 'old_label': '8.i1', 'projective_image': '1600.9849', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.i1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546529
    {'ambient': '1600.9849', 'aut_centralizer_order': 40, 'aut_label': '8.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '160.236', 'aut_weyl_index': 160, 'centralizer': '80.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1'], 'contains': ['16.b1', '16.f1', '16.h1', '40.a1', '40.c1'], 'core': '16.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [871, -1, 1178, -1], 'generators': [1, 320, 800, 400, 1296], 'label': '1600.9849.8.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.j1', 'projective_image': '800.1194', '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': '40.12'}
  • id: 79546530
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '8.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '800.1199', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1'], 'contains': ['16.c1', '16.f1', '16.h1', '40.b1', '40.d1'], 'core': '16.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [1259, -1, 703, -1], 'generators': [1, 800, 336, 1412, 320], 'label': '1600.9849.8.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '8.k1', 'projective_image': '800.1194', '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': '200.42'}
  • id: 79546531
    {'ambient': '1600.9849', 'aut_centralizer_order': 20, 'aut_label': '8.l1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '640.19253', 'aut_weyl_index': 40, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1'], 'contains': ['16.b1', '16.g1', '40.f1', '40.i1'], 'core': '16.b1', 'coset_action_label': None, 'count': 2, 'diagramx': [6586, -1, 9384, -1], 'generators': [1307, 320, 800, 400, 976], 'label': '1600.9849.8.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '8.l1', 'projective_image': '800.1194', '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': '80.50'}
  • id: 79546532
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '8.m1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '3200.w', 'aut_weyl_index': 8, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1'], 'contains': ['16.c1', '16.g1', '40.h1'], 'core': '16.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [6811, -1, 8672, -1], 'generators': [1307, 800, 976, 1412, 320], 'label': '1600.9849.8.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '8.m1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.m1', 'subgroup_fusion': None, 'weyl_group': '400.210'}
  • id: 79546533
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': ['800.b1', '800.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '4.k1', '4.l1', '4.m1', '10.a1'], 'core': '2.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [4088, 7236, 3335, 7289], 'generators': [1, 336, 400, 4, 2, 320, 800], 'label': '1600.9849.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1', '4.k1', '4.l1', '4.m1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546534
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '8.n1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '400.207', 'aut_weyl_index': 64, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.a1', '4.q1'], 'contains': ['16.d1', '16.j1', '16.m1', '200.m1'], 'core': '16.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [4103, -1, 3553, -1], 'generators': [3, 4, 656, 40, 320], 'label': '1600.9849.8.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.n1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.n1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546535
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '8.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '400.207', 'aut_weyl_index': 64, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.d1', '4.q1'], 'contains': ['16.d1', '16.l1', '16.m1', '40.r1'], 'core': '16.d1', 'coset_action_label': None, 'count': 16, 'diagramx': [3909, -1, 2768, -1], 'generators': [1, 4, 336, 2, 320], 'label': '1600.9849.8.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.o1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.o1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546536
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '8.p1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.g1', '4.q1'], 'contains': ['16.e1', '16.j1', '16.l1', '40.s1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [6062, -1, 6661, -1], 'generators': [41, 1012, 336, 2, 320], 'label': '1600.9849.8.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.p1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.p1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546537
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '8.q1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.o1', '4.q1'], 'contains': ['16.e1', '16.m1', '200.q1'], 'core': '16.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [4789, -1, 5497, -1], 'generators': [3, 4, 336, 362, 320], 'label': '1600.9849.8.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.o1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '8.q1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.q1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546538
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '320.1595', 'aut_weyl_index': 80, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.c1'], 'contains': ['20.a1', '20.b1', '20.g1', '20.i1', '20.j1', '50.c1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2700, -1, 2526, -1], 'generators': [1, 336, 400, 4, 2, 800], 'label': '1600.9849.10.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '10.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546540
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '16.a1', 'aut_quo_index': 5040, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'contains': ['32.a1', '32.b1', '32.c1', '80.e1', '80.f1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5890, 5017, 6487, 5138], 'generators': [1012, 336, 320, 800], 'label': '1600.9849.16.a1', 'mobius_quo': 0, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1', '8.e1', '8.f1', '8.g1', '8.h1'], 'normal_contains': ['32.a1', '32.b1', '32.c1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '800.1194', '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': '400.207'}
  • id: 79546541
    {'ambient': '1600.9849', 'aut_centralizer_order': 400, 'aut_label': '16.b1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '64.101', 'aut_weyl_index': 400, 'centralizer': '16.b1', 'complements': ['100.q1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.j1', '8.l1'], 'contains': ['32.a1', '80.g1', '80.h1'], 'core': '16.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5486, 6806, 5907, 7440], 'generators': [400, 320, 800, 336], 'label': '1600.9849.16.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.c1'], 'normal_contains': ['32.a1', '400.a1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '800.1194', 'quotient_action_image': '16.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 79546542
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '16.c1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '1600.10254', 'aut_weyl_index': 16, 'centralizer': '400.a1', 'complements': ['100.q1'], 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '8.k1', '8.m1'], 'contains': ['32.a1', '80.k1', '80.l1'], 'core': '16.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5139, 5861, 5685, 6487], 'generators': [1412, 336, 320, 800], 'label': '1600.9849.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.c1'], 'normal_contains': ['32.a1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '800.1194', 'quotient_action_image': '16.13', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546543
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '16.d1', 'aut_quo_index': 4, 'aut_stab_index': 4, 'aut_weyl_group': '400.207', 'aut_weyl_index': 64, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.a1', '8.i1', '8.n1', '8.o1'], 'contains': ['32.b1', '32.d1', '80.m1'], 'core': '16.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [3429, 3694, 2548, 3721], 'generators': [1, 336, 320, 1012], 'label': '1600.9849.16.d1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': ['8.a1', '8.i1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.d1', 'projective_image': '1600.9849', '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': '400.207'}
  • id: 79546544
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6400.fg', 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': ['800.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.e1', '4.g1', '4.o1', '4.q1', '50.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 2, 'diagramx': [4753, 3245, 4167, 3269], 'generators': [1, 336, 40, 800, 2, 320, 4], 'label': '1600.9849.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.e1', '4.g1', '4.o1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546545
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '16.e1', 'aut_quo_index': 4, 'aut_stab_index': 2, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.e1', '8.i1', '8.p1', '8.q1'], 'contains': ['32.b1', '80.q1'], 'core': '16.e1', 'coset_action_label': None, 'count': 2, 'diagramx': [5687, 2874, 6284, 2895], 'generators': [41, 336, 320, 1012], 'label': '1600.9849.16.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.e1', 'normal_contained_in': ['8.e1', '8.i1'], 'normal_contains': ['32.b1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': '1600.9849', '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': '400.207'}
  • id: 79546546
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '16.f1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '80.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '8.j1', '8.k1'], 'contains': ['32.a1', '32.d1', '80.a1', '80.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [760, -1, 1329, -1], 'generators': [1, 320, 1296, 800], 'label': '1600.9849.16.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.f1', 'projective_image': '800.1194', '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': '40.12'}
  • id: 79546547
    {'ambient': '1600.9849', 'aut_centralizer_order': 40, 'aut_label': '16.g1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '160.203', 'aut_weyl_index': 160, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.l1', '8.m1'], 'contains': ['32.a1', '32.e1', '80.c1', '80.d1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7010, -1, 9384, -1], 'generators': [1307, 320, 976, 800], 'label': '1600.9849.16.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '16.g1', 'projective_image': '800.1194', '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': '80.50'}
  • id: 79546548
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '16.h1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '80.g1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '8.j1', '8.k1'], 'contains': ['32.a1', '80.i1', '80.j1'], 'core': '32.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1437, -1, 596, -1], 'generators': [401, 800, 1296, 320], 'label': '1600.9849.16.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.h1', 'projective_image': '800.1194', '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': '40.12'}
  • id: 79546549
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '16.i1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '400.207', 'aut_weyl_index': 64, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1'], 'contains': ['32.c1', '32.d1', '80.n1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [2394, -1, 2204, -1], 'generators': [1, 336, 320, 212], 'label': '1600.9849.16.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '16.i1', 'projective_image': '1600.9849', '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': '200.42'}
  • id: 79546550
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '16.j1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '8.n1', '8.p1'], 'contains': ['32.b1', '32.e1', '80.o1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6692, -1, 7207, -1], 'generators': [1307, 976, 320, 1012], 'label': '1600.9849.16.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.j1', 'projective_image': '1600.9849', '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': '400.207'}
  • id: 79546551
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '16.k1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1'], 'contains': ['32.c1', '32.e1', '80.p1'], 'core': '32.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [7205, -1, 8940, -1], 'generators': [1307, 976, 320, 212], 'label': '1600.9849.16.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.f1', 'old_label': '16.k1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.k1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546552
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '16.l1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '8.o1', '8.p1'], 'contains': ['32.b1', '80.r1', '80.s1'], 'core': '32.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [6111, -1, 6124, -1], 'generators': [2, 336, 320, 4], 'label': '1600.9849.16.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.l1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.l1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546553
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '16.m1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '400.207', 'aut_weyl_index': 64, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '8.n1', '8.o1', '8.q1'], 'contains': ['32.b1', '80.t1'], 'core': '32.b1', 'coset_action_label': None, 'count': 8, 'diagramx': [4587, -1, 3479, -1], 'generators': [3, 336, 320, 4], 'label': '1600.9849.16.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.d1', 'old_label': '16.m1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.m1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546554
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '16.n1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1'], 'contains': ['32.c1', '80.u1'], 'core': '32.c1', 'coset_action_label': None, 'count': 2, 'diagramx': [8071, -1, 8159, -1], 'generators': [441, 336, 320, 212], 'label': '1600.9849.16.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.h1', 'old_label': '16.n1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.n1', 'subgroup_fusion': None, 'weyl_group': '200.44'}
  • id: 79546555
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6400.fg', 'aut_weyl_index': 4, 'centralizer': '400.a1', 'complements': ['800.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.e1', '4.j1', '4.n1', '50.e1'], 'core': '2.e1', 'coset_action_label': None, 'count': 1, 'diagramx': [3394, 2279, 3695, 2296], 'generators': [1, 336, 400, 1012, 40, 320, 800], 'label': '1600.9849.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.e1', '4.j1', '4.n1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '400.207'}
  • id: 79546556
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.b1', '10.a1'], 'contains': ['40.a1', '40.b1', '40.c1', '40.d1', '40.e1', '40.j1', '40.l1', '100.b1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1238, -1, 1587, -1], 'generators': [1, 1012, 800, 400, 336], 'label': '1600.9849.20.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546557
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '10.a1'], 'contains': ['40.e1', '40.n1', '40.p1', '40.r1', '100.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3146, -1, 2142, -1], 'generators': [1, 800, 4, 2, 336], 'label': '1600.9849.20.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546558
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.g1', '10.b1'], 'contains': ['40.g1', '40.m1', '40.o1', '40.s1', '100.g1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8611, -1, 7740, -1], 'generators': [41, 800, 1012, 674, 656], 'label': '1600.9849.20.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '20.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546560
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '20.e1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '160.207', 'aut_weyl_index': 160, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.i1', '10.b1'], 'contains': ['40.f1', '40.g1', '40.h1', '40.i1', '40.k1', '100.i1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8132, -1, 8960, -1], 'generators': [1307, 340, 800, 400, 656], 'label': '1600.9849.20.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '20.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.e1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546561
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '20.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.j1', '10.b1'], 'contains': ['40.k1', '40.m1', '40.q1', '100.j1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9089, -1, 7970, -1], 'generators': [41, 1012, 800, 400, 656], 'label': '1600.9849.20.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.j1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '20.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.f1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546562
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '20.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '160.207', 'aut_weyl_index': 160, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.k1', '10.a1'], 'contains': ['40.j1', '40.n1', '100.k1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [3764, -1, 2623, -1], 'generators': [2, 4, 800, 400, 336], 'label': '1600.9849.20.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.g1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546563
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '20.h1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '160.207', 'aut_weyl_index': 160, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.k1', '10.b1'], 'contains': ['40.k1', '40.o1', '100.k1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7951, -1, 7545, -1], 'generators': [2, 4, 800, 400, 656], 'label': '1600.9849.20.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.k1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '20.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.h1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546564
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '20.i1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '160.207', 'aut_weyl_index': 160, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['4.l1', '10.a1'], 'contains': ['40.j1', '40.p1', '100.l1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2623, -1, 2480, -1], 'generators': [3, 4, 800, 400, 336], 'label': '1600.9849.20.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.l1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.i1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546565
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '20.j1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['4.m1', '10.a1'], 'contains': ['40.l1', '40.n1', '40.p1', '100.m1'], 'core': '800.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3419, -1, 2337, -1], 'generators': [401, 4, 800, 2, 336], 'label': '1600.9849.20.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.m1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '20.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.j1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546566
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.f1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '6400.fg', 'aut_weyl_index': 4, 'centralizer': '800.a1', 'complements': ['800.b1', '800.c1'], 'conjugacy_class_count': 2, 'contained_in': ['1.a1'], 'contains': ['4.f1', '4.g1', '4.m1', '4.n1', '4.o1', '50.f1'], 'core': '2.f1', 'coset_action_label': None, 'count': 2, 'diagramx': [5507, 4104, 5197, 4134], 'generators': [401, 336, 440, 4, 2, 320, 800], 'label': '1600.9849.2.f1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.f1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.f1', '4.g1', '4.m1', '4.n1', '4.o1'], 'normalizer': '1.a1', 'old_label': '2.f1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.f1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546567
    {'ambient': '1600.9849', 'aut_centralizer_order': 4, 'aut_label': '25.a1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '256.29080', 'aut_weyl_index': 100, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['50.a1', '50.b1', '50.c1', '50.d1', '50.e1', '50.f1', '50.g1', '50.h1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [6131, -1, 5291, -1], 'generators': [1, 674, 40, 400], 'label': '1600.9849.25.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '25.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '25.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546568
    {'ambient': '1600.9849', 'aut_centralizer_order': 800, 'aut_label': '32.a1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '32.11', 'aut_weyl_index': 800, 'centralizer': '16.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1', '16.f1', '16.g1', '16.h1'], 'contains': ['64.a1', '160.a1', '160.b1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5226, 5636, 5641, 6067], 'generators': [800, 320, 336], 'label': '1600.9849.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['64.a1', '800.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '800.1194', 'quotient_action_image': '16.13', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '16.13'}
  • id: 79546569
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '32.b1', 'aut_quo_index': 48, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.d1', '16.e1', '16.j1', '16.l1', '16.m1'], 'contains': ['64.a1', '160.g1', '160.h1'], 'core': '32.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5548, 4230, 5842, 4344], 'generators': [1012, 320, 336], 'label': '1600.9849.32.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.b1', 'normal_contained_in': ['16.a1', '16.d1', '16.e1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.b1', 'projective_image': '1600.9849', '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': '400.207'}
  • id: 79546570
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '32.c1', 'aut_quo_index': 30, 'aut_stab_index': 1, 'aut_weyl_group': '800.1191', 'aut_weyl_index': 32, 'centralizer': '400.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.i1', '16.k1', '16.n1'], 'contains': ['64.a1', '160.i1', '160.j1'], 'core': '32.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [6610, 5017, 6843, 5138], 'generators': [212, 320, 336], 'label': '1600.9849.32.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '32.c1', 'normal_contained_in': ['16.a1'], 'normal_contains': ['64.a1'], 'normalizer': '1.a1', 'old_label': '32.c1', 'projective_image': '1600.9849', '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': '400.207'}
  • id: 79546571
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '80.g1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.d1', '16.f1', '16.i1'], 'contains': ['64.a1', '160.c1', '160.d1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [2347, -1, 2548, -1], 'generators': [1, 1296, 320], 'label': '1600.9849.32.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '32.d1', 'projective_image': '1600.9849', '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': '40.12'}
  • id: 79546572
    {'ambient': '1600.9849', 'aut_centralizer_order': 40, 'aut_label': '32.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '80.30', 'aut_weyl_index': 320, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['16.g1', '16.j1', '16.k1'], 'contains': ['64.a1', '160.e1', '160.f1'], 'core': '64.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [6980, -1, 8387, -1], 'generators': [1307, 976, 320], 'label': '1600.9849.32.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.g1', 'old_label': '32.e1', 'projective_image': '1600.9849', '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': '40.12'}
  • id: 79546573
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '16.10', 'aut_weyl_index': 1600, 'centralizer': '40.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '20.a1'], 'contains': ['80.a1', '80.g1', '80.i1', '200.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [115, -1, 1071, -1], 'generators': [1, 336, 800, 400], 'label': '1600.9849.40.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
  • id: 79546574
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.k1', '20.a1'], 'contains': ['80.a1', '80.j1', '80.k1', '200.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1087, -1, 333, -1], 'generators': [1, 800, 336, 1412], 'label': '1600.9849.40.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.b1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546575
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '40.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.j1', '20.a1'], 'contains': ['80.b1', '80.g1', '80.j1', '200.a1'], 'core': '400.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [418, -1, 835, -1], 'generators': [1, 800, 1296, 400], 'label': '1600.9849.40.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.c1', 'old_label': '40.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546576
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.d1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.k1', '20.a1'], 'contains': ['80.b1', '80.i1', '80.k1', '200.b1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [719, -1, 94, -1], 'generators': [1, 800, 1296, 1412], 'label': '1600.9849.40.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.d1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546577
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.g1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '800.a1', 'complements': ['800.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.g1', '4.h1', '4.i1', '4.j1', '4.k1', '10.b1'], 'core': '2.g1', 'coset_action_label': None, 'count': 1, 'diagramx': [6860, 8079, 6816, 8138], 'generators': [41, 336, 400, 1012, 2, 320, 800], 'label': '1600.9849.2.g1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.g1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.g1', '4.h1', '4.i1', '4.j1', '4.k1'], 'normalizer': '1.a1', 'old_label': '2.g1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.g1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546578
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '40.e1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.a1', '20.a1', '20.b1'], 'contains': ['80.a1', '80.b1', '80.e1', '80.m1', '80.n1', '200.c1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [1589, -1, 1583, -1], 'generators': [1, 800, 336, 1012], 'label': '1600.9849.40.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.e1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546579
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '40.f1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '32.25', 'aut_weyl_index': 800, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '20.e1'], 'contains': ['80.c1', '80.h1', '200.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [7367, -1, 9766, -1], 'generators': [1307, 656, 800, 400], 'label': '1600.9849.40.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.f1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.f1', 'subgroup_fusion': None, 'weyl_group': '16.10'}
  • id: 79546580
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '40.g1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.b1', '20.c1', '20.d1', '20.e1'], 'contains': ['80.c1', '80.d1', '80.f1', '80.o1', '80.p1', '200.d1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8922, -1, 9130, -1], 'generators': [1307, 800, 656, 340], 'label': '1600.9849.40.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.g1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.g1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546581
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.h1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '80.50', 'aut_weyl_index': 320, 'centralizer': '800.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.m1', '20.e1'], 'contains': ['80.c1', '80.d1', '80.l1', '200.f1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [7870, -1, 9585, -1], 'generators': [1307, 800, 656, 740], 'label': '1600.9849.40.h1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.h1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.h1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546582
    {'ambient': '1600.9849', 'aut_centralizer_order': 80, 'aut_label': '40.i1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '160.207', 'aut_weyl_index': 160, 'centralizer': '160.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.l1', '20.e1'], 'contains': ['80.d1', '80.h1', '200.e1'], 'core': '400.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [7668, -1, 9944, -1], 'generators': [1035, 800, 976, 400], 'label': '1600.9849.40.i1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.i1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.g1', 'old_label': '40.i1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.i1', 'subgroup_fusion': None, 'weyl_group': '80.50'}
  • id: 79546583
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '40.j1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '20.a1', '20.g1', '20.i1'], 'contains': ['80.e1', '80.g1', '80.k1', '200.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2043, -1, 2031, -1], 'generators': [400, 800, 336, 1012], 'label': '1600.9849.40.j1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.j1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.j1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546584
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '40.k1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1', '20.e1', '20.f1', '20.h1'], 'contains': ['80.f1', '80.h1', '80.l1', '200.g1'], 'core': '400.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [8293, -1, 8554, -1], 'generators': [400, 800, 656, 1012], 'label': '1600.9849.40.k1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.k1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.k1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546585
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '40.l1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '200.a1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.d1', '20.a1', '20.j1'], 'contains': ['80.e1', '80.i1', '80.j1', '200.h1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [2260, -1, 1816, -1], 'generators': [401, 800, 336, 1012], 'label': '1600.9849.40.l1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.l1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.l1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546586
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '40.m1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '200.e1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1', '20.c1', '20.f1'], 'contains': ['80.f1', '80.q1', '200.i1'], 'core': '800.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9154, -1, 7981, -1], 'generators': [41, 1012, 656, 800], 'label': '1600.9849.40.m1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.m1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.m1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546587
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.n1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '20.b1', '20.g1', '20.j1'], 'contains': ['80.e1', '80.r1', '200.j1'], 'core': '800.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3523, -1, 2932, -1], 'generators': [2, 4, 336, 800], 'label': '1600.9849.40.n1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.n1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.n1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546588
    {'ambient': '1600.9849', 'aut_centralizer_order': 2, 'aut_label': '2.h1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 2, 'centralizer': '800.a1', 'complements': ['800.b1', '800.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.j1', '4.l1', '4.o1', '4.p1', '50.h1'], 'core': '2.h1', 'coset_action_label': None, 'count': 1, 'diagramx': [6580, 4757, 5693, 4793], 'generators': [3, 336, 400, 4, 362, 320, 800], 'label': '1600.9849.2.h1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.h1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.j1', '4.l1', '4.o1', '4.p1'], 'normalizer': '1.a1', 'old_label': '2.h1', 'projective_image': '800.1194', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.h1', 'subgroup_fusion': None, 'weyl_group': '800.1194'}
  • id: 79546589
    {'ambient': '1600.9849', 'aut_centralizer_order': 32, 'aut_label': '40.o1', 'aut_quo_index': None, 'aut_stab_index': 20, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['8.f1', '20.c1', '20.d1', '20.h1'], 'contains': ['80.f1', '80.s1', '200.j1'], 'core': '800.a1', 'coset_action_label': None, 'count': 20, 'diagramx': [8629, -1, 7556, -1], 'generators': [2, 4, 656, 800], 'label': '1600.9849.40.o1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.o1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.o1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546590
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.p1', 'aut_quo_index': None, 'aut_stab_index': 40, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.g1', '20.b1', '20.i1', '20.j1'], 'contains': ['80.e1', '80.t1', '200.k1'], 'core': '800.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [2957, -1, 2719, -1], 'generators': [3, 4, 336, 800], 'label': '1600.9849.40.p1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.a1', 'old_label': '40.p1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.p1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546591
    {'ambient': '1600.9849', 'aut_centralizer_order': 64, 'aut_label': '40.q1', 'aut_quo_index': None, 'aut_stab_index': 10, 'aut_weyl_group': '40.12', 'aut_weyl_index': 640, 'centralizer': '400.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.h1', '20.d1', '20.f1'], 'contains': ['80.f1', '80.u1', '200.l1'], 'core': '800.a1', 'coset_action_label': None, 'count': 10, 'diagramx': [9885, -1, 8768, -1], 'generators': [441, 212, 656, 800], 'label': '1600.9849.40.q1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.h1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '10.b1', 'old_label': '40.q1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.q1', 'subgroup_fusion': None, 'weyl_group': '40.12'}
  • id: 79546592
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '40.r1', 'aut_quo_index': None, 'aut_stab_index': 160, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.b1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['8.o1', '20.b1'], 'contains': ['80.m1', '80.r1', '80.t1', '200.n1'], 'core': '1600.a1', 'coset_action_label': '40T1457', 'count': 160, 'diagramx': [3226, -1, 2376, -1], 'generators': [1, 4, 336, 2], 'label': '1600.9849.40.r1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.b1', 'old_label': '40.r1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.r1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546593
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '40.s1', 'aut_quo_index': None, 'aut_stab_index': 80, 'aut_weyl_group': '20.3', 'aut_weyl_index': 1280, 'centralizer': '400.c1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.p1', '20.c1'], 'contains': ['80.o1', '80.q1', '80.s1', '200.p1'], 'core': '1600.a1', 'coset_action_label': '40T1437', 'count': 80, 'diagramx': [6851, -1, 7769, -1], 'generators': [41, 1012, 656, 674], 'label': '1600.9849.40.s1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.g1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.c1', 'old_label': '40.s1', 'projective_image': '1600.9849', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.s1', 'subgroup_fusion': None, 'weyl_group': '20.3'}
  • id: 79546594
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '50.a1', 'aut_quo_index': None, 'aut_stab_index': 100, 'aut_weyl_group': '32.51', 'aut_weyl_index': 800, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1', '25.a1'], 'contains': ['100.a1', '100.c1', '100.d1', '100.f1', '100.h1', '100.m1', '100.p1'], 'core': '800.a1', 'coset_action_label': None, 'count': 100, 'diagramx': [5340, -1, 5013, -1], 'generators': [401, 674, 40], 'label': '1600.9849.50.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.a1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546595
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '50.b1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '64.261', 'aut_weyl_index': 400, 'centralizer': '400.d1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.b1', '25.a1'], 'contains': ['100.a1', '100.b1', '100.f1', '100.i1', '100.l1'], 'core': '400.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4704, -1, 5258, -1], 'generators': [3, 680, 400], 'label': '1600.9849.50.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.b1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 79546596
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '50.c1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '32.46', 'aut_weyl_index': 800, 'centralizer': '200.c1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['10.a1', '25.a1'], 'contains': ['100.b1', '100.d1', '100.k1', '100.l1', '100.m1'], 'core': '400.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4422, -1, 4082, -1], 'generators': [1, 2, 400], 'label': '1600.9849.50.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.c1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546597
    {'ambient': '1600.9849', 'aut_centralizer_order': 8, 'aut_label': '50.d1', 'aut_quo_index': None, 'aut_stab_index': 50, 'aut_weyl_group': '64.202', 'aut_weyl_index': 400, 'centralizer': '200.j1', 'complements': None, 'conjugacy_class_count': 2, 'contained_in': ['2.d1', '25.a1'], 'contains': ['100.a1', '100.d1', '100.e1', '100.g1', '100.o1', '100.q1'], 'core': '800.a1', 'coset_action_label': None, 'count': 50, 'diagramx': [4985, -1, 4725, -1], 'generators': [1, 674, 40, 800], 'label': '1600.9849.50.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.d1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 79546598
    {'ambient': '1600.9849', 'aut_centralizer_order': 16, 'aut_label': '50.e1', 'aut_quo_index': None, 'aut_stab_index': 25, 'aut_weyl_group': '64.202', 'aut_weyl_index': 400, 'centralizer': '200.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.e1', '25.a1'], 'contains': ['100.b1', '100.c1', '100.e1', '100.j1', '100.n1'], 'core': '400.a1', 'coset_action_label': None, 'count': 25, 'diagramx': [3260, -1, 3783, -1], 'generators': [1, 40, 400], 'label': '1600.9849.50.e1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '25.a1', 'old_label': '50.e1', 'projective_image': '800.1194', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '50.e1', 'subgroup_fusion': None, 'weyl_group': '8.5'}