Abstract group data - 896.5502

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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': '14.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [6, 14, 2, 2, 2, 2, 2, 4], 'aut_gens': [[11467436, 19232857, 5128257, 7304270, 12188737, 18125889, 30581825, 6204507], [6276539, 17045571, 5128257, 20291662, 12188737, 20290625, 6210625, 19232857], [11467436, 30578766, 5128257, 12167252, 18125889, 10024001, 19208257, 11081817], [32774817, 19232857, 18125889, 20291662, 31664193, 5128257, 30581825, 6204507], [19042990, 19232857, 10024001, 12173390, 7292993, 29499457, 30581825, 6204507], [9433772, 19232857, 5128257, 7304270, 12188737, 18125889, 30581825, 6204507], [5837497, 19232857, 12188737, 10012750, 5128257, 31664193, 30581825, 6204507], [5850796, 19232857, 5128257, 7304270, 12188737, 18125889, 30581825, 6204507], [11447993, 32754777, 12188737, 12173390, 5128257, 31664193, 30581825, 17070171]], 'aut_group': '10752.cb', 'aut_hash': 7784500158005166103, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10752, 'aut_permdeg': 200, 'aut_perms': [659092179503017877037324366569073631913771081430924897884213631089600877688064805200847872388927262724269361020552897152938435007691745479347009785253111251011820398128481097245160196223218832590738187086294501403199980944959028843947210003765606627013172353238773864369918320887914619347607905905315439597321816579156191787761734706889138476682141366316568719882998477609733, 7423640901430007663030849392825348692568735107901614430639785520396091377500704736926510877268284853983641489184121605454615203179987982313055427155235503588702798258977677888165330321805547043458421210849916500075509301377976227126363807088333821684919546951913827201989784505348931539183949361947956826324435209870119314001307006349329556863632820152128761995258115869336, 711306402389776790704837990905595759196413132274705278548860626308142467104803672052235226447418611264160052449901262187332076507321888856347270432244857644292078106697627721937327321886126807679798866535342457448288042093653149501406776665517639697041060083365503344029706665157250823929651471387569173974053837570616215306992247353557282765182142071396804198935565161855313, 558507316140761146179253775528422653481501286824092153997887599032047144863825180615009012573855711966346956312830656681119693310461261984589744817066641604181160813256306911357649376477504959365608430758903384092286842246188075097173514887308542663315618406501913959137765367974189101302109290905046217350583870140677746526997003028117022004266839078296553226409907787496096, 684553674759033580914722138945518044582655041872960523967306092510712283279264774023109791852001790550392744838019602882990143635332899859651575450612400015769497905400364875184630227878364305532119953620397348526749479330663485209356900815707888259685457530253571099790925509567648445203869051322236348744222152801318364629527404753985989117059449297177434419178551939907410, 734882348606588659139581706625718797068878653916800068734046952580399087959357615223681599022455257707954423957647298314281881554949810085241714962634765437370385764151628646675108286575574808371506534977720910390069537408853218146715358805139250592278949817606943623779751564465933290171029905300369077523263479475216610683408190157794243147635351131193680653150049604555215, 446246490580176636272981761593013350837677257350729307131625365058149496388093049674821623784901986230697032409023625436938813371506705744892175699688676867558678069231305726637638499184730250053132850568981234030246347324390972037509636451367931631282271544173972309680190476551071913058829168247117100384829344049462909730452738596766965567344507592280069656574406830424062, 499994274042378167541217723598683653303550068987298119252895803702593058332334152762166801369429562242259927025899554971605488053125189631215358464358779574482969607752621354290322170124576091442755326001707823743633915488549941967643037361597539241938255450189772178091542651125520089028837696834970777403089308782924651745818377294362639698463344460732261092641658233537431], 'aut_phi_ratio': 28.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [2, 8, 1, 1], [2, 14, 4, 1], [4, 56, 1, 1], [7, 64, 3, 2], [14, 64, 3, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:F_8:A_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '10752.cb', 'autcentquo_hash': 7784500158005166103, 'autcentquo_nilpotent': False, 'autcentquo_order': 10752, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^4:F_8:A_4', 'cc_stats': [[1, 1, 1], [2, 7, 1], [2, 8, 1], [2, 14, 4], [4, 56, 1], [7, 64, 6], [14, 64, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '896.5502', 'commutator_count': 1, 'commutator_label': '64.267', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5502, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 7, 1, 1], [2, 8, 1, 1], [2, 14, 1, 4], [4, 56, 1, 1], [7, 64, 6, 1], [14, 64, 6, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 48, 'exponent': 28, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[14, 1, 4]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '112.41', 'hash': 5502, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [7, 2, 2, 4, 2, 2, 2, 2], 'inner_gens': [[11467436, 6199382, 5128257, 18152539, 31664193, 29499457, 32746561, 8943683], [30743203, 19232857, 29499457, 31659086, 20290625, 10024001, 30581825, 6204507], [11467436, 11081817, 5128257, 10012750, 12188737, 18125889, 30581825, 32752731], [9414329, 11081817, 12188737, 7304270, 5128257, 31664193, 30581825, 32752731], [32779948, 11081817, 5128257, 10012750, 12188737, 18125889, 30581825, 32752731], [7884460, 11081817, 5128257, 10012750, 12188737, 18125889, 30581825, 32752731], [9433772, 19232857, 5128257, 7304270, 12188737, 18125889, 30581825, 6204507], [7876276, 19232857, 31664193, 29498446, 18125889, 12188737, 30581825, 6204507]], 'inner_hash': 5502, 'inner_nilpotent': False, 'inner_order': 896, 'inner_split': True, 'inner_tex': 'C_2^4:F_8', 'inner_used': [1, 2, 3], 'irrC_degree': 14, 'irrQ_degree': 14, 'irrQ_dim': 14, 'irrR_degree': 14, 'irrep_stats': [[1, 14], [7, 2], [14, 4]], 'label': '896.5502', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^4:F8', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 20, 'number_divisions': 10, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 61, 'number_subgroup_classes': 263, 'number_subgroups': 3542, 'old_label': None, 'order': 896, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 71], [4, 56], [7, 384], [14, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [3, 2, 2], 'outer_gen_pows': [5128257, 17043521, 17043521], 'outer_gens': [[6276539, 17045571, 5128257, 20291662, 12188737, 20290625, 6210625, 19232857], [11467436, 8367193, 5128257, 12173390, 12188737, 18125889, 30581825, 11079771], [11467436, 30590041, 5128257, 20291662, 12188737, 18125889, 30581825, 30592091]], 'outer_group': '12.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 4, 'outer_perms': [4, 16, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'A_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [6, 2], [7, 2], [14, 4]], 'representations': {'PC': {'code': '108571499057859365861811391874258145268334803568832576', 'gens': [1, 3, 4, 5, 6, 7, 8], 'pres': [8, -2, -7, -2, 2, 2, 2, 2, 2, 16, 2690, 7402, 23299, 4491, 6164, 4492, 29573, 15133, 16470, 8638, 8967, 10767]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [11467436, 19232857, 5128257, 7304270, 12188737, 18125889, 30581825, 6204507]}, 'Perm': {'d': 16, 'gens': [11212821043200, 101156429848, 9709968821183, 11536, 2789792426303, 5606234750016, 2789792421136, 1313941673647]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [14], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^4:F_8', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
• gps_conj_classes •

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

  
  
  • id: 111100668
    {'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 5502, 'group_order': 896, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 17043521, 'size': 1}
  • id: 111100679
    {'aut_label': '2A', 'centralizer': '7.a1', 'counter': 2, 'group_counter': 5502, 'group_order': 896, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8941633, 'size': 7}
  • id: 111100681
    {'aut_label': '2B', 'centralizer': '8.a1', 'counter': 3, 'group_counter': 5502, 'group_order': 896, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 5128257, 'size': 8}
  • id: 111100682
    {'aut_label': '2C', 'centralizer': '14.a1', 'counter': 4, 'group_counter': 5502, 'group_order': 896, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 17056852, 'size': 14}
  • id: 111100683
    {'aut_label': '2C', 'centralizer': '14.a1', 'counter': 5, 'group_counter': 5502, 'group_order': 896, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 8922196, 'size': 14}
  • id: 111100684
    {'aut_label': '2C', 'centralizer': '14.a1', 'counter': 6, 'group_counter': 5502, 'group_order': 896, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 8930380, 'size': 14}
  • id: 111100685
    {'aut_label': '2C', 'centralizer': '14.a1', 'counter': 7, 'group_counter': 5502, 'group_order': 896, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 8924246, 'size': 14}
  • id: 111100686
    {'aut_label': '4A', 'centralizer': '56.g1', 'counter': 8, 'group_counter': 5502, 'group_order': 896, 'label': '4A', 'order': 4, 'powers': [2, 8, 8], 'representative': 29507673, 'size': 56}
  • id: 111100687
    {'aut_label': '7A1', 'centralizer': '64.a1', 'counter': 9, 'group_counter': 5502, 'group_order': 896, 'label': '7A1', 'order': 7, 'powers': [11, 13, 1], 'representative': 17732355, 'size': 64}
  • id: 111100669
    {'aut_label': '7A-1', 'centralizer': '64.a1', 'counter': 10, 'group_counter': 5502, 'group_order': 896, 'label': '7A-1', 'order': 7, 'powers': [12, 14, 1], 'representative': 17371630, 'size': 64}
  • id: 111100670
    {'aut_label': '7A1', 'centralizer': '64.a1', 'counter': 11, 'group_counter': 5502, 'group_order': 896, 'label': '7A2', 'order': 7, 'powers': [14, 10, 1], 'representative': 17109435, 'size': 64}
  • id: 111100671
    {'aut_label': '7A-1', 'centralizer': '64.a1', 'counter': 12, 'group_counter': 5502, 'group_order': 896, 'label': '7A-2', 'order': 7, 'powers': [13, 9, 1], 'representative': 17797881, 'size': 64}
  • id: 111100672
    {'aut_label': '7A-1', 'centralizer': '64.a1', 'counter': 13, 'group_counter': 5502, 'group_order': 896, 'label': '7A3', 'order': 7, 'powers': [10, 11, 1], 'representative': 16946006, 'size': 64}
  • id: 111100673
    {'aut_label': '7A1', 'centralizer': '64.a1', 'counter': 14, 'group_counter': 5502, 'group_order': 896, 'label': '7A-3', 'order': 7, 'powers': [9, 12, 1], 'representative': 17011372, 'size': 64}
  • id: 111100674
    {'aut_label': '14A1', 'centralizer': '64.a1', 'counter': 15, 'group_counter': 5502, 'group_order': 896, 'label': '14A1', 'order': 14, 'powers': [9, 17, 3], 'representative': 4833964, 'size': 64}
  • id: 111100675
    {'aut_label': '14A-1', 'centralizer': '64.a1', 'counter': 16, 'group_counter': 5502, 'group_order': 896, 'label': '14A-1', 'order': 14, 'powers': [10, 18, 3], 'representative': 4768598, 'size': 64}
  • id: 111100676
    {'aut_label': '14A-1', 'centralizer': '64.a1', 'counter': 17, 'group_counter': 5502, 'group_order': 896, 'label': '14A3', 'order': 14, 'powers': [13, 20, 3], 'representative': 4571897, 'size': 64}
  • id: 111100677
    {'aut_label': '14A1', 'centralizer': '64.a1', 'counter': 18, 'group_counter': 5502, 'group_order': 896, 'label': '14A-3', 'order': 14, 'powers': [14, 19, 3], 'representative': 5194171, 'size': 64}
  • id: 111100678
    {'aut_label': '14A-1', 'centralizer': '64.a1', 'counter': 19, 'group_counter': 5502, 'group_order': 896, 'label': '14A5', 'order': 14, 'powers': [12, 15, 3], 'representative': 4407790, 'size': 64}
  • id: 111100680
    {'aut_label': '14A1', 'centralizer': '64.a1', 'counter': 20, 'group_counter': 5502, 'group_order': 896, 'label': '14A-5', 'order': 14, 'powers': [11, 16, 3], 'representative': 4506371, 'size': 64}
• 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: 4853445
    {'cdim': 1, 'counter': 1, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.1a', '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], 'schur_index': 1}
  • id: 4853447
    {'cdim': 1, 'counter': 2, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.1b', '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], 'schur_index': 1}
  • id: 4853448
    {'cdim': 1, 'counter': 3, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.1c', 'multiplicity': 6, 'nt': [7, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
  • id: 4853449
    {'cdim': 1, 'counter': 4, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.1d', 'multiplicity': 6, 'nt': [14, 1], 'qdim': 6, 'qvalues': [6, 6, -6, 6, 6, 6, 6, -6, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
  • id: 4853450
    {'cdim': 7, 'counter': 5, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.7a', 'multiplicity': 1, 'nt': [8, 25], 'qdim': 7, 'qvalues': [7, 7, 7, -1, -1, -1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4853451
    {'cdim': 7, 'counter': 6, 'faithful': False, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.7b', 'multiplicity': 1, 'nt': [14, 9], 'qdim': 7, 'qvalues': [7, 7, -7, -1, -1, -1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4853452
    {'cdim': 14, 'counter': 7, 'faithful': True, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.14a', 'multiplicity': 1, 'nt': [16, 1075], 'qdim': 14, 'qvalues': [14, -2, 0, -2, -2, -2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4853453
    {'cdim': 14, 'counter': 8, 'faithful': True, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.14b', 'multiplicity': 1, 'nt': [16, 1075], 'qdim': 14, 'qvalues': [14, -2, 0, -2, -2, 6, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4853454
    {'cdim': 14, 'counter': 9, 'faithful': True, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.14c', 'multiplicity': 1, 'nt': [16, 1075], 'qdim': 14, 'qvalues': [14, -2, 0, -2, 6, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
  • id: 4853446
    {'cdim': 14, 'counter': 10, 'faithful': True, 'group': '896.5502', 'group_order': 896, 'image': None, 'label': '896.5502.14d', 'multiplicity': 1, 'nt': [16, 1075], 'qdim': 14, 'qvalues': [14, -2, 0, 6, -2, -2, -2, 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: 7999024
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1', 'kernel_order': 896, 'label': '896.5502.1a', '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]]]}
  • id: 7999035
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1', 'kernel_order': 448, 'label': '896.5502.1b', '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]]]}
  • id: 7999037
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 3, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c1', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 3]], [[1, -1]], [[1, -3]], [[1, -2]], [[1, -1]], [[1, 3]], [[1, 2]], [[1, 1]]]}
  • id: 7999038
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 4, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c2', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -3]], [[1, 1]], [[1, 3]], [[1, 2]], [[1, 1]], [[1, -3]], [[1, -2]], [[1, -1]]]}
  • id: 7999039
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 5, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c3', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -2]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -3]], [[1, -2]], [[1, 1]], [[1, -3]], [[1, 2]], [[1, -1]], [[1, 3]]]}
  • id: 7999040
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 6, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c4', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 2]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 3]], [[1, 2]], [[1, -1]], [[1, 3]], [[1, -2]], [[1, 1]], [[1, -3]]]}
  • id: 7999041
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 7, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c5', 'nt': [7, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -1]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, 3]], [[1, -2]]]}
  • id: 7999042
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 8, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '7.1', 'image_order': 7, 'indicator': 0, 'kernel': '7.a1', 'kernel_order': 128, 'label': '896.5502.1c6', 'nt': [7, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 1]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -1]], [[1, -2]], [[1, 1]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, -3]], [[1, 2]]]}
  • id: 7999043
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 9, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d1', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -3]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 3]], [[1, -1]], [[-1, -3]], [[-1, -2]], [[-1, -1]], [[-1, 3]], [[-1, 2]], [[-1, 1]]]}
  • id: 7999025
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 10, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d2', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 3]], [[1, -2]], [[1, -1]], [[1, 2]], [[1, -3]], [[1, 1]], [[-1, 3]], [[-1, 2]], [[-1, 1]], [[-1, -3]], [[-1, -2]], [[-1, -1]]]}
  • id: 7999026
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 11, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d3', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -2]], [[1, -1]], [[1, 3]], [[1, 1]], [[1, 2]], [[1, -3]], [[-1, -2]], [[-1, 1]], [[-1, -3]], [[-1, 2]], [[-1, -1]], [[-1, 3]]]}
  • id: 7999027
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 12, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d4', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 2]], [[1, 1]], [[1, -3]], [[1, -1]], [[1, -2]], [[1, 3]], [[-1, 2]], [[-1, -1]], [[-1, 3]], [[-1, -2]], [[-1, 1]], [[-1, -3]]]}
  • id: 7999028
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 13, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d5', 'nt': [14, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, -1]], [[1, 3]], [[1, -2]], [[1, -3]], [[1, 1]], [[1, 2]], [[-1, -1]], [[-1, -3]], [[-1, 2]], [[-1, 1]], [[-1, 3]], [[-1, -2]]]}
  • id: 7999029
    {'center': '1.a1', 'center_index': 1, 'center_order': 896, 'counter': 14, 'cyclotomic_n': 7, 'dim': 1, 'faithful': False, 'field': [1, -1, 1, -1, 1, -1, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '14.2', 'image_order': 14, 'indicator': 0, 'kernel': '14.a1', 'kernel_order': 64, 'label': '896.5502.1d6', 'nt': [14, 6], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[1, -3]], [[1, 2]], [[1, 3]], [[1, -1]], [[1, -2]], [[-1, 1]], [[-1, 3]], [[-1, -2]], [[-1, -1]], [[-1, -3]], [[-1, 2]]]}
  • id: 7999030
    {'center': '56.a1', 'center_index': 56, 'center_order': 16, 'counter': 15, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '56.11', 'image_order': 56, 'indicator': 1, 'kernel': '56.a1', 'kernel_order': 16, 'label': '896.5502.7a', 'nt': [8, 25], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7999031
    {'center': '56.a1', 'center_index': 56, 'center_order': 16, 'counter': 16, 'cyclotomic_n': 1, 'dim': 7, 'faithful': False, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '112.41', 'image_order': 112, 'indicator': 1, 'kernel': '112.a1', 'kernel_order': 8, 'label': '896.5502.7b', 'nt': [14, 9], 'q_character': None, 'values': [[[7, 0]], [[7, 0]], [[-7, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7999032
    {'center': '896.a1', 'center_index': 896, 'center_order': 1, 'counter': 17, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '896.5502', 'image_order': 896, 'indicator': 1, 'kernel': '896.a1', 'kernel_order': 1, 'label': '896.5502.14a', 'nt': [16, 1075], 'q_character': None, 'values': [[[14, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[-2, 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]]]}
  • id: 7999033
    {'center': '896.a1', 'center_index': 896, 'center_order': 1, 'counter': 18, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '896.5502', 'image_order': 896, 'indicator': 1, 'kernel': '896.a1', 'kernel_order': 1, 'label': '896.5502.14b', 'nt': [16, 1075], 'q_character': None, 'values': [[[14, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7999034
    {'center': '896.a1', 'center_index': 896, 'center_order': 1, 'counter': 19, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '896.5502', 'image_order': 896, 'indicator': 1, 'kernel': '896.a1', 'kernel_order': 1, 'label': '896.5502.14c', 'nt': [16, 1075], 'q_character': None, 'values': [[[14, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
  • id: 7999036
    {'center': '896.a1', 'center_index': 896, 'center_order': 1, 'counter': 20, 'cyclotomic_n': 1, 'dim': 14, 'faithful': True, 'field': [0, 1], 'group': '896.5502', 'group_counter': 5502, 'group_order': 896, 'image': None, 'image_isoclass': '896.5502', 'image_order': 896, 'indicator': 1, 'kernel': '896.a1', 'kernel_order': 1, 'label': '896.5502.14d', 'nt': [16, 1075], 'q_character': None, 'values': [[[14, 0]], [[-2, 0]], [[0, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
• 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: 68994365
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 896, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 14, 'label': '896.5502.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '896.5502', 'subgroup_hash': 5502, 'subgroup_order': 896, 'subgroup_tex': 'C_2^4:F_8', 'supersolvable': False, 'sylow': 0}
  • id: 68994376
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': True, 'core_order': 448, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '896.5502.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '448.1393', 'subgroup_hash': 1393, 'subgroup_order': 448, 'subgroup_tex': 'C_2^3:F_8', 'supersolvable': False, 'sylow': 0}
  • id: 68994387
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 2, 'label': '896.5502.7.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '7.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.1578', 'subgroup_hash': 1578, 'subgroup_order': 128, 'subgroup_tex': 'C_2^3\\wr C_2', 'supersolvable': True, 'sylow': 2}
  • id: 68994398
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 4, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.8.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.41', 'subgroup_hash': 41, 'subgroup_order': 112, 'subgroup_tex': 'C_2\\times F_8', 'supersolvable': False, 'sylow': 0}
  • id: 68994409
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': True, 'core_order': 64, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '896.5502.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.267', 'subgroup_hash': 267, 'subgroup_order': 64, 'subgroup_tex': 'C_2^6', 'supersolvable': True, 'sylow': 0}
  • id: 68994420
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68994423
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.14.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14.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': 14, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68994424
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
  • id: 68994425
    {'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 1, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.11', 'subgroup_hash': 11, 'subgroup_order': 56, 'subgroup_tex': 'F_8', 'supersolvable': False, 'sylow': 0}
  • id: 68994366
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
  • id: 68994367
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 68994368
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
  • id: 68994369
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
  • id: 68994370
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '28.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': 28, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
  • id: 68994371
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': True, 'core_order': 16, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '896.5502.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.11', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 11, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'F_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994372
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994373
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994374
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.b3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.b3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994375
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.b4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.b4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994377
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 68994378
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 68994379
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994380
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994381
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.e3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.e3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994382
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
  • id: 68994383
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.56.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '56.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': 56, 'quotient_simple': 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: 68994384
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 27, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '896.5502.64.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '64.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
  • id: 68994385
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '896.5502.112.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.41', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 41, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times F_8', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S', 'C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
  • id: 68994386
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994388
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994389
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994390
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994391
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994392
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994393
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.c6', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.c6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994394
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994395
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994396
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994397
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.e3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.e3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994399
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994400
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.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': 112, 'quotient_simple': 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: 68994401
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994402
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994403
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994404
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g5', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g5', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994405
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.112.g6', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '112.g6', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 112, 'quotient_simple': 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: 68994406
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 14, 'characteristic': False, 'core_order': 1, 'counter': 47, 'cyclic': True, 'direct': None, 'hall': 7, 'label': '896.5502.128.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
  • id: 68994407
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 68994408
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 68994410
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.b2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 68994411
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.b3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.b3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 68994412
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 52, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '896.5502.224.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 68994413
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 68994414
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.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': 224, 'quotient_simple': 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: 68994415
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.e2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e2', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 68994416
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.e3', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e3', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 68994417
    {'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '896.5502.224.e4', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '224.e4', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 224, 'quotient_simple': 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: 68994418
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 58, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '896.5502.448.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, '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: 68994419
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': False, 'core_order': 1, 'counter': 59, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '896.5502.448.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, '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: 68994421
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 60, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '896.5502.448.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '448.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': 448, '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: 68994422
    {'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '896.5502', 'ambient_counter': 5502, 'ambient_order': 896, 'ambient_tex': 'C_2^4:F_8', 'central': True, 'central_factor': False, 'centralizer_order': 896, 'characteristic': True, 'core_order': 1, 'counter': 61, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '896.5502.896.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '896.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '896.5502', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5502, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 896, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^4:F_8', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'PC', 'U0', 'D2', 'C4'], '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: 68994424
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '448.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '8.a1'], 'contains': ['112.a1', '128.a1'], 'core': '112.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9477, -1, 2293, -1], 'generators': [30581825, 19895041, 6210625, 19208257], 'label': '896.5502.16.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '16.a1', 'projective_image': '896.5502', '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': '56.11'}
  • id: 68994425
    {'ambient': '896.5502', 'aut_centralizer_order': 1, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '896.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['2.a1'], 'contains': ['112.g1', '128.a1'], 'core': '896.a1', 'coset_action_label': '16T1075', 'count': 64, 'diagramx': [8606, -1, 688, -1], 'generators': [11086932, 19232857, 8384590, 19895041], 'label': '896.5502.16.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1', 'old_label': '16.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '56.11'}
  • id: 68994365
    {'ambient': '896.5502', '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': '896.a1', 'complements': ['896.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '7.a1', '8.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8606, 2384, 3041, 3541], 'generators': [19221588, 12188737, 30581825, 6210625, 30590041, 19895041, 19208257, 8384590], 'label': '896.5502.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '7.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '896.5502', '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': '896.5502'}
  • id: 68994366
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '28.a1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.b1'], 'contains': ['56.c1', '56.d1', '56.e1'], 'core': '896.a1', 'coset_action_label': '28T101', 'count': 56, 'diagramx': [7903, -1, 6376, -1], 'generators': [12188737, 11084886, 19221588, 6210625, 19208257], 'label': '896.5502.28.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '28.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68994367
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '28.b1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['14.a1'], 'contains': ['56.b1', '56.b2', '56.b3', '56.b4', '56.e1', '56.e2', '56.e3'], 'core': '896.a1', 'coset_action_label': '28T97', 'count': 56, 'diagramx': [4921, -1, 4454, -1], 'generators': [30590041, 8384590, 19221588, 6210625, 19208257], 'label': '896.5502.28.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '28.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994368
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '28.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 56, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.b1'], 'contains': ['56.a1', '56.c1', '56.f1', '56.g1'], 'core': '56.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8537, -1, 7369, -1], 'generators': [12188737, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.28.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 68994369
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '28.d1', 'aut_quo_index': None, 'aut_stab_index': 21, 'aut_weyl_group': '64.267', 'aut_weyl_index': 168, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['14.b1', '14.c1'], 'contains': ['56.d1', '56.f1', '56.g1'], 'core': '112.a1', 'coset_action_label': None, 'count': 21, 'diagramx': [7212, -1, 8405, -1], 'generators': [31672409, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.28.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.d1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.d1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 68994370
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '28.e1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['14.a1', '14.b1', '14.c1'], 'contains': ['56.e1', '56.e2', '56.e3', '56.f1'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [6445, -1, 5609, -1], 'generators': [30590041, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.28.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '28.e1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994371
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '56.a1', 'complements': ['16.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '28.c1'], 'contains': ['112.a1', '112.d1'], 'core': '56.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9117, 4192, 7369, 7512], 'generators': [12188737, 30581825, 6210625, 19208257], 'label': '896.5502.56.a1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '56.a1', 'normal_contained_in': ['7.a1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '56.a1', 'projective_image': '896.5502', 'quotient_action_image': '56.11', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '56.11'}
  • id: 68994372
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.b1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['28.b1'], 'contains': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c5', '112.g2', '112.g3', '112.g4', '112.g5'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3253, -1, 4340, -1], 'generators': [30590041, 8384590, 17056852, 6210625], 'label': '896.5502.56.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994373
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.b2', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1'], 'contains': ['112.c1', '112.c2', '112.c6', '112.g2', '112.g3', '112.g4', '112.g6'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [932, -1, 3245, -1], 'generators': [8384590, 17056852, 32754777, 6210625], 'label': '896.5502.56.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.b2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994374
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.b3', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['28.b1'], 'contains': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c6', '112.g2', '112.g3', '112.g4', '112.g5', '112.g6'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1947, -1, 3735, -1], 'generators': [8384590, 19221588, 32754777, 6210625], 'label': '896.5502.56.b3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.b3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994375
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.b4', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.b1'], 'contains': ['112.c1', '112.c3', '112.c5', '112.g1', '112.g4', '112.g5', '112.g6'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [3918, -1, 2754, -1], 'generators': [30590041, 8384590, 19221588, 6210625], 'label': '896.5502.56.b4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.b4', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994376
    {'ambient': '896.5502', 'aut_centralizer_order': 1, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '10752.cb', 'aut_weyl_index': 1, 'centralizer': '896.a1', 'complements': ['448.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '16.a1', '16.b1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8606, 3014, 3041, 4354], 'generators': [30590041, 8384590, 30581825, 19221588, 19895041, 6210625, 19208257], 'label': '896.5502.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['14.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '896.5502', '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': '896.5502'}
  • id: 68994377
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '56.c1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 672, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['28.a1', '28.c1'], 'contains': ['112.b1', '112.d1', '112.e1', '112.f1'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [8698, -1, 8028, -1], 'generators': [12188737, 19221588, 6210625, 19208257], 'label': '896.5502.56.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68994378
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '56.d1', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '16.14', 'aut_weyl_index': 672, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['28.a1', '28.d1'], 'contains': ['112.e1', '112.f1'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [7620, -1, 8776, -1], 'generators': [19221588, 7279702, 6210625, 19208257], 'label': '896.5502.56.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '56.d1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68994379
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.e1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '6.2', 'aut_weyl_index': 1792, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['28.a1', '28.b1', '28.e1'], 'contains': ['112.c2', '112.c3', '112.e1'], 'core': '896.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [6445, -1, 6076, -1], 'generators': [11084886, 19221588, 6210625, 19208257], 'label': '896.5502.56.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.e1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994380
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.e2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['28.b1', '28.e1'], 'contains': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c5', '112.c6', '112.e1', '112.e2'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5357, -1, 5094, -1], 'generators': [30590041, 19221588, 6210625, 19208257], 'label': '896.5502.56.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.e2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994381
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.e3', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['28.b1', '28.e1'], 'contains': ['112.c1', '112.c2', '112.c3', '112.c4', '112.e1', '112.e2', '112.e3'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6132, -1, 5585, -1], 'generators': [30590041, 6204507, 6210625, 19208257], 'label': '896.5502.56.e3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '56.e3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.e3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994382
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.f1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1', '28.d1', '28.e1'], 'contains': ['112.a1', '112.e1', '112.e2', '112.e3'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7247, -1, 6878, -1], 'generators': [30581825, 19221588, 6210625, 19208257], 'label': '896.5502.56.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.f1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994383
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '56.g1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '24.13', 'aut_weyl_index': 448, 'centralizer': '56.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['28.c1', '28.d1'], 'contains': ['112.a1', '112.f1'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [8137, -1, 9584, -1], 'generators': [30581825, 6210625, 29520980, 19208257], 'label': '896.5502.56.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '56.g1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.g1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
  • id: 68994384
    {'ambient': '896.5502', 'aut_centralizer_order': 56, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1'], 'contains': ['128.a1', '448.b1'], 'core': '896.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9878, -1, 210, -1], 'generators': [5534478, 12188737], 'label': '896.5502.64.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1', 'old_label': '64.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994385
    {'ambient': '896.5502', 'aut_centralizer_order': 512, 'aut_label': '112.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '7.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '56.a1', '56.f1', '56.g1'], 'contains': ['224.d1'], 'core': '112.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8468, 4192, 8040, 7512], 'generators': [30581825, 6210625, 19208257], 'label': '896.5502.112.a1', 'mobius_quo': -1, 'mobius_sub': -8, 'normal_closure': '112.a1', 'normal_contained_in': ['14.a1', '56.a1'], 'normal_contains': ['896.a1'], 'normalizer': '1.a1', 'old_label': '112.a1', 'projective_image': '896.5502', 'quotient_action_image': '7.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '112.a1', 'subgroup_fusion': None, 'weyl_group': '7.1'}
  • id: 68994386
    {'ambient': '896.5502', 'aut_centralizer_order': 24, 'aut_label': '112.b1', 'aut_quo_index': None, 'aut_stab_index': 112, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.c1'], 'contains': ['224.a1', '224.b1', '224.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 112, 'diagramx': [8763, -1, 8991, -1], 'generators': [12188737, 19221588, 6210625], 'label': '896.5502.112.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1', 'old_label': '112.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68994387
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '7.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1344.11689', 'aut_weyl_index': 8, 'centralizer': '112.a1', 'complements': ['128.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '14.c1'], 'core': '7.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7629, 740, 5813, 1388], 'generators': [12188737, 30590041, 8384590, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.7.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['14.a1', '56.a1'], 'normalizer': '1.a1', 'old_label': '7.a1', 'projective_image': '896.5502', 'quotient_action_image': '7.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '112.41'}
  • id: 68994388
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b2', '56.b3', '56.b4', '56.e2', '56.e3'], 'contains': ['224.b2', '224.b3', '224.e1', '224.e2', '224.e3', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3325, -1, 4604, -1], 'generators': [30590041, 6204507, 6210625], 'label': '896.5502.112.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994389
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c2', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b2', '56.b3', '56.e1', '56.e2', '56.e3'], 'contains': ['224.b1', '224.b2', '224.b3', '224.e1', '224.e2', '224.e3'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3760, -1, 5585, -1], 'generators': [30590041, 32766036, 6210625], 'label': '896.5502.112.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994390
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c3', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b3', '56.b4', '56.e1', '56.e2', '56.e3'], 'contains': ['224.b1', '224.b2', '224.b3', '224.e1', '224.e2', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [5387, -1, 5094, -1], 'generators': [30590041, 19221588, 6210625], 'label': '896.5502.112.c3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994391
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c4', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b3', '56.e2', '56.e3'], 'contains': ['224.b2', '224.b3', '224.e1', '224.e2'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [4746, -1, 6076, -1], 'generators': [8365147, 30590041, 6210625], 'label': '896.5502.112.c4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c4', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994392
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c5', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.b1', '56.b4', '56.e2'], 'contains': ['224.b2', '224.e1', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4349, -1, 4113, -1], 'generators': [8365147, 11084886, 8941633], 'label': '896.5502.112.c5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c5', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c5', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994393
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.c6', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.b2', '56.b3', '56.e2'], 'contains': ['224.b2', '224.e2', '224.e3'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [1279, -1, 3622, -1], 'generators': [11084886, 6204507, 8941633], 'label': '896.5502.112.c6', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.c6', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.c6', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994394
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.d1', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '56.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.a1', '56.c1'], 'contains': ['224.a1', '224.d1'], 'core': '896.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [9057, -1, 8531, -1], 'generators': [12188737, 6210625, 19208257], 'label': '896.5502.112.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '112.d1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68994395
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.e1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['56.c1', '56.d1', '56.e1', '56.e2', '56.e3', '56.f1'], 'contains': ['224.b1', '224.b2', '224.b3', '224.d1'], 'core': '896.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [7170, -1, 7058, -1], 'generators': [19221588, 6210625, 19208257], 'label': '896.5502.112.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '112.e1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994396
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.e2', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['56.e2', '56.e3', '56.f1'], 'contains': ['224.b2', '224.b3', '224.d1'], 'core': '896.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [6662, -1, 6567, -1], 'generators': [32741452, 6210625, 19208257], 'label': '896.5502.112.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.e2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994397
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.e3', 'aut_quo_index': None, 'aut_stab_index': 14, 'aut_weyl_group': '12.3', 'aut_weyl_index': 896, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['56.e3', '56.f1'], 'contains': ['224.b3', '224.d1'], 'core': '896.a1', 'coset_action_label': None, 'count': 14, 'diagramx': [7544, -1, 7549, -1], 'generators': [6204507, 6210625, 19208257], 'label': '896.5502.112.e3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.e3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.e3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994398
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '168.43', 'aut_weyl_index': 64, 'centralizer': '448.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['16.a1', '56.a1', '64.a1'], 'core': '56.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [9549, -1, 2293, -1], 'generators': [12188737, 30581825, 19895041, 6210625, 19208257], 'label': '896.5502.8.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '8.a1', 'projective_image': '896.5502', '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': '56.11'}
  • id: 68994399
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.f1', 'aut_quo_index': None, 'aut_stab_index': 42, 'aut_weyl_group': '4.2', 'aut_weyl_index': 2688, 'centralizer': '56.g1', 'complements': None, 'conjugacy_class_count': 3, 'contained_in': ['56.c1', '56.d1', '56.g1'], 'contains': ['224.c1', '224.d1'], 'core': '896.a1', 'coset_action_label': None, 'count': 42, 'diagramx': [8041, -1, 9614, -1], 'generators': [6210625, 29520980, 19208257], 'label': '896.5502.112.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.b1', 'old_label': '112.f1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.f1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
  • id: 68994400
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '21.1', 'aut_weyl_index': 512, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['16.b1', '56.b4'], 'contains': ['224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [5865, -1, 676, -1], 'generators': [11086932, 19232857, 8384590], 'label': '896.5502.112.g1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1', 'old_label': '112.g1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g1', 'subgroup_fusion': None, 'weyl_group': '7.1'}
  • id: 68994401
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g2', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.b1', '56.b2', '56.b3'], 'contains': ['224.e1', '224.e2', '224.e3'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [122, -1, 3131, -1], 'generators': [30590041, 8384590, 17056852], 'label': '896.5502.112.g2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.g2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994402
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g3', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.b1', '56.b2', '56.b3'], 'contains': ['224.e1', '224.e2', '224.e3'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [496, -1, 2640, -1], 'generators': [30590041, 8922196, 8384590], 'label': '896.5502.112.g3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.g3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994403
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g4', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b2', '56.b3', '56.b4'], 'contains': ['224.e1', '224.e2', '224.e3', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [1642, -1, 1658, -1], 'generators': [30590041, 8362068, 8384590], 'label': '896.5502.112.g4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.g4', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994404
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g5', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['56.b1', '56.b3', '56.b4'], 'contains': ['224.e1', '224.e2', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [2455, -1, 2149, -1], 'generators': [30590041, 8384590, 19221588], 'label': '896.5502.112.g5', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.g5', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g5', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994405
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '112.g6', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['56.b2', '56.b3', '56.b4'], 'contains': ['224.e2', '224.e3', '224.e4'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [943, -1, 1167, -1], 'generators': [8384590, 19221588, 32754777], 'label': '896.5502.112.g6', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '112.g6', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '112.g6', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994406
    {'ambient': '896.5502', 'aut_centralizer_order': 56, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '64.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '64.a1'], 'contains': ['896.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [9564, -1, 216, -1], 'generators': [19895041], 'label': '896.5502.128.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1', 'old_label': '128.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994407
    {'ambient': '896.5502', 'aut_centralizer_order': 192, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1', '112.d1'], 'contains': ['448.a1', '448.b1'], 'core': '896.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8767, -1, 8285, -1], 'generators': [12188737, 6210625], 'label': '896.5502.224.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1', 'old_label': '224.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994408
    {'ambient': '896.5502', 'aut_centralizer_order': 192, 'aut_label': '224.b1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.b1', '112.c2', '112.c3', '112.e1'], 'contains': ['448.a1', '448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [7026, -1, 6322, -1], 'generators': [19221588, 6210625], 'label': '896.5502.224.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '224.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994409
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '14.a1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '168.53', 'aut_weyl_index': 64, 'centralizer': '14.a1', 'complements': ['64.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.b1', '28.e1'], 'core': '14.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6605, 1918, 4885, 2871], 'generators': [30590041, 8384590, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.14.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.a1', 'normal_contained_in': ['2.a1', '7.a1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '14.a1', 'projective_image': '896.5502', 'quotient_action_image': '14.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '14.2'}
  • id: 68994410
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.b2', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c5', '112.c6', '112.e1', '112.e2'], 'contains': ['448.a1', '448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [5357, -1, 5340, -1], 'generators': [32741452, 8375361], 'label': '896.5502.224.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.b2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994411
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.b3', 'aut_quo_index': None, 'aut_stab_index': 84, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['112.c1', '112.c2', '112.c3', '112.c4', '112.e1', '112.e2', '112.e3'], 'contains': ['448.a1', '448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 84, 'diagramx': [6445, -1, 5831, -1], 'generators': [32741452, 6210625], 'label': '896.5502.224.b3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.b3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.b3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994412
    {'ambient': '896.5502', 'aut_centralizer_order': 192, 'aut_label': '224.c1', 'aut_quo_index': None, 'aut_stab_index': 28, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5376, 'centralizer': '56.g1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.b1', '112.f1'], 'contains': ['448.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 28, 'diagramx': [8331, -1, 8991, -1], 'generators': [6210625, 29520980], 'label': '896.5502.224.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '28.c1', 'old_label': '224.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
  • id: 68994413
    {'ambient': '896.5502', 'aut_centralizer_order': 512, 'aut_label': '224.d1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['112.a1', '112.d1', '112.e1', '112.e2', '112.e3', '112.f1'], 'contains': ['448.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7968, -1, 7549, -1], 'generators': [6210625, 19208257], 'label': '896.5502.224.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '112.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '224.d1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994414
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.e1', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c5', '112.g2', '112.g3', '112.g4', '112.g5'], 'contains': ['448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [3616, -1, 4113, -1], 'generators': [30590041, 6197332], 'label': '896.5502.224.e1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.e1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994415
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.e2', 'aut_quo_index': None, 'aut_stab_index': 168, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['112.c1', '112.c2', '112.c3', '112.c4', '112.c6', '112.g2', '112.g3', '112.g4', '112.g5', '112.g6'], 'contains': ['448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 168, 'diagramx': [2237, -1, 3622, -1], 'generators': [30590041, 19221588], 'label': '896.5502.224.e2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.e2', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e2', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994416
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.e3', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.c1', '112.c2', '112.c6', '112.g2', '112.g3', '112.g4', '112.g6'], 'contains': ['448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [860, -1, 3131, -1], 'generators': [30590041, 17070171], 'label': '896.5502.224.e3', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.e3', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e3', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994417
    {'ambient': '896.5502', 'aut_centralizer_order': 64, 'aut_label': '224.e4', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '3.1', 'aut_weyl_index': 3584, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['112.c1', '112.c3', '112.c5', '112.g1', '112.g4', '112.g5', '112.g6'], 'contains': ['448.c1'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4414, -1, 2395, -1], 'generators': [30590041, 6204507], 'label': '896.5502.224.e4', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '224.e4', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.e4', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994418
    {'ambient': '896.5502', 'aut_centralizer_order': 1536, 'aut_label': '448.a1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '7.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['224.a1', '224.b1', '224.b2', '224.b3', '224.c1', '224.d1'], 'contains': ['896.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7968, -1, 6322, -1], 'generators': [6210625], 'label': '896.5502.448.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '112.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '448.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994419
    {'ambient': '896.5502', 'aut_centralizer_order': 1344, 'aut_label': '448.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '8.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '224.a1'], 'contains': ['896.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [8767, -1, 4544, -1], 'generators': [12188737], 'label': '896.5502.448.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1', 'old_label': '448.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994420
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '14.b1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 56, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['28.a1', '28.c1', '28.d1', '28.e1'], 'core': '56.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7740, -1, 5992, -1], 'generators': [12188737, 30590041, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.14.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.b1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
  • id: 68994421
    {'ambient': '896.5502', 'aut_centralizer_order': 192, 'aut_label': '448.c1', 'aut_quo_index': None, 'aut_stab_index': 56, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10752, 'centralizer': '14.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['224.b1', '224.b2', '224.b3', '224.e1', '224.e2', '224.e3', '224.e4'], 'contains': ['896.a1'], 'core': '896.a1', 'coset_action_label': None, 'count': 56, 'diagramx': [4704, -1, 4113, -1], 'generators': [19221588], 'label': '896.5502.448.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '14.a1', 'old_label': '448.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '448.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994422
    {'ambient': '896.5502', 'aut_centralizer_order': None, 'aut_label': '896.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': ['128.a1', '448.a1', '448.b1', '448.c1'], 'contains': [], 'core': '896.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8403, 9260, 4328, 9354], 'generators': [], 'label': '896.5502.896.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '896.a1', 'normal_contained_in': ['112.a1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '896.a1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '896.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
  • id: 68994423
    {'ambient': '896.5502', 'aut_centralizer_order': 8, 'aut_label': '14.c1', 'aut_quo_index': None, 'aut_stab_index': 7, 'aut_weyl_group': '192.1540', 'aut_weyl_index': 56, 'centralizer': '112.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['7.a1'], 'contains': ['28.d1', '28.e1'], 'core': '112.a1', 'coset_action_label': None, 'count': 7, 'diagramx': [7048, -1, 7076, -1], 'generators': [30590041, 20291662, 30581825, 19221588, 6210625, 19208257], 'label': '896.5502.14.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '7.a1', 'old_label': '14.c1', 'projective_image': '896.5502', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.c1', 'subgroup_fusion': None, 'weyl_group': '16.14'}