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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 4, 4, 4, 6], 'aut_gens': [[85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345214, 1, 1800200723874894, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345215, 1, 737186240310024, 1821883084207920, 795340005803406, 5621224034334630, 1558054095215088, 1822337812123926, 795533260057254], [2670559180032990, 1, 2730880140856584, 4088283555510366, 4466613169859766, 1822038947023848, 1821696294042054, 359890668365808, 795533260057254], [3353416120037551, 1, 3292827135187014, 795788474029920, 360096412929840, 4088283555510366, 3437629559701230, 359890668365808, 795533260057254], [4913965112744520, 1, 2353504295850726, 735925055088, 795203061792528, 3437629559701230, 4934975208295326, 795533260057254, 1822337812123926]], 'aut_group': '6144.ze', 'aut_hash': 4158378184127417885, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 48, 'aut_perms': [9994073346956691326310842053270612521722600417121765690395696, 11053973361945428615465185065217005606706706163177450420395046, 3820124437949437479010256854732253317884941161210171750861093, 6009849731016979477797640346594027687778683254932669762820388, 1059547849389346313480217742049924904175648835892817432484552], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 2, 2], [2, 24, 2, 1], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 2], [4, 24, 2, 1], [4, 48, 4, 1], [6, 128, 1, 1], [8, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^3:(C_2^2\\times S_4)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '3072.bgb', 'autcentquo_hash': 7983714371117797868, 'autcentquo_nilpotent': False, 'autcentquo_order': 3072, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^3:(C_2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 4], [2, 24, 2], [3, 128, 1], [4, 12, 2], [4, 24, 4], [4, 48, 4], [6, 128, 1], [8, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '384.18135', 'commutator_count': 1, 'commutator_label': '192.1023', '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', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1090131, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['384.18135', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 4], [2, 24, 1, 2], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 4], [4, 48, 1, 4], [6, 128, 1, 1], [8, 48, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '192.1538', 'hash': 1090131, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 1, 3, 2, 2, 2, 2, 2, 2], 'inner_gens': [[85621839894847, 1, 84307934393430, 1821883084207920, 795340005803406, 3846242716609368, 1558054095215088, 1822337812123926, 795533260057254], [85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [21010095550807, 1, 25057722413880, 795340005803406, 1821883084207920, 1558054095215088, 3846242716609368, 795533260057254, 1822337812123926], [733176358717801, 1, 1799920432122126, 359728823398326, 795340005803406, 2208813870141024, 4466613169859766, 359890668365808, 795533260057254], [85621839894847, 1, 441265441118040, 359728823398326, 795340005803406, 4088283555510366, 3437629559701230, 359890668365808, 795533260057254], [1663625494874185, 1, 3865752002090880, 312321447414, 360096412929840, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 1226009285991720, 795788474029920, 735925055088, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345215, 1, 1800200723874894, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 441097551912486, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254]], 'inner_hash': 18135, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': True, 'inner_tex': 'C_4^2:S_4', 'inner_used': [1, 3, 4, 6], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 2], [12, 4]], 'label': '768.1090131', 'linC_count': 2, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:S4', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 24, 'number_divisions': 24, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 273, 'number_subgroup_classes': 528, 'number_subgroups': 5446, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 103], [3, 128], [4, 312], [6, 128], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[85621839894846, 1, 25057722413880, 312321447414, 735925055088, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 25057722413880, 2208813870141024, 3437629559701230, 312321447414, 735925055088, 359890668365808, 795533260057254], [85621839894846, 1, 25057722413880, 312321447414, 735925055088, 2208813870141024, 3437629559701230, 359890668365808, 795533260057254], [85621839894847, 1, 25057722413880, 312321447414, 735925055088, 2208813870141024, 3437629559701230, 359890668365808, 795533260057254]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 289, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 12], [6, 2], [12, 4]], 'representations': {'PC': {'code': '79924844233235786991899159435981848360229194954850928243109730413695879780301013992512', 'gens': [1, 2, 4, 5, 6, 8], 'pres': [9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 181, 46, 218, 1299, 444, 345, 823, 157, 36941, 18158, 3263, 1976, 365, 158, 30246, 12111, 7584, 12967, 12112, 7801, 1762, 2059, 214, 19457, 1970]}, 'Perm': {'d': 18, 'gens': [85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:S_4', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 110944298
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1090131, 'group_order': 768, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
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id: 110944309
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1090131, 'group_order': 768, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 1, 'size': 1}
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id: 110944315
{'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 1090131, 'group_order': 768, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 359890668365809, 'size': 3}
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id: 110944316
{'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 1090131, 'group_order': 768, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 359890668365808, 'size': 3}
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id: 110944317
{'aut_label': '2D', 'centralizer': '12.h1.a1', 'counter': 5, 'group_counter': 1090131, 'group_order': 768, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 312321447415, 'size': 12}
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id: 110944318
{'aut_label': '2D', 'centralizer': '12.h1.b1', 'counter': 6, 'group_counter': 1090131, 'group_order': 768, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 1179562541714329, 'size': 12}
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id: 110944319
{'aut_label': '2F', 'centralizer': '12.h1.a1', 'counter': 7, 'group_counter': 1090131, 'group_order': 768, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 735925055088, 'size': 12}
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id: 110944320
{'aut_label': '2F', 'centralizer': '12.h1.b1', 'counter': 8, 'group_counter': 1090131, 'group_order': 768, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 2208813870141024, 'size': 12}
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id: 110944321
{'aut_label': '2H', 'centralizer': '24.d1.a1', 'counter': 9, 'group_counter': 1090131, 'group_order': 768, 'label': '2H', 'order': 2, 'powers': [1, 9], 'representative': 4047630492624, 'size': 24}
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id: 110944299
{'aut_label': '2H', 'centralizer': '24.d1.a1', 'counter': 10, 'group_counter': 1090131, 'group_order': 768, 'label': '2I', 'order': 2, 'powers': [1, 10], 'representative': 4047630492625, 'size': 24}
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id: 110944300
{'aut_label': '3A', 'centralizer': '128.a1.a1', 'counter': 11, 'group_counter': 1090131, 'group_order': 768, 'label': '3A', 'order': 3, 'powers': [11, 1], 'representative': 1603223196513150, 'size': 128}
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id: 110944301
{'aut_label': '4A', 'centralizer': '12.k1.a1', 'counter': 12, 'group_counter': 1090131, 'group_order': 768, 'label': '4A', 'order': 4, 'powers': [4, 12], 'representative': 1179668884439071, 'size': 12}
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id: 110944302
{'aut_label': '4B', 'centralizer': '12.k1.a1', 'counter': 13, 'group_counter': 1090131, 'group_order': 768, 'label': '4B', 'order': 4, 'powers': [4, 13], 'representative': 5620794243692664, 'size': 12}
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id: 110944303
{'aut_label': '4C', 'centralizer': '24.c1.a1', 'counter': 14, 'group_counter': 1090131, 'group_order': 768, 'label': '4C', 'order': 4, 'powers': [4, 14], 'representative': 381193590973254, 'size': 24}
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id: 110944304
{'aut_label': '4C', 'centralizer': '24.c1.a1', 'counter': 15, 'group_counter': 1090131, 'group_order': 768, 'label': '4D', 'order': 4, 'powers': [4, 15], 'representative': 381193590973255, 'size': 24}
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id: 110944305
{'aut_label': '4E', 'centralizer': '24.r1.a1', 'counter': 16, 'group_counter': 1090131, 'group_order': 768, 'label': '4E', 'order': 4, 'powers': [4, 16], 'representative': 1179762397854126, 'size': 24}
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id: 110944306
{'aut_label': '4F', 'centralizer': '24.r1.a1', 'counter': 17, 'group_counter': 1090131, 'group_order': 768, 'label': '4F', 'order': 4, 'powers': [4, 17], 'representative': 1179762397854127, 'size': 24}
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id: 110944307
{'aut_label': '4G', 'centralizer': '48.f1.a1', 'counter': 18, 'group_counter': 1090131, 'group_order': 768, 'label': '4G', 'order': 4, 'powers': [7, 18], 'representative': 85895741411455, 'size': 48}
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id: 110944308
{'aut_label': '4G', 'centralizer': '48.f1.a1', 'counter': 19, 'group_counter': 1090131, 'group_order': 768, 'label': '4H', 'order': 4, 'powers': [7, 19], 'representative': 439907893140360, 'size': 48}
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id: 110944310
{'aut_label': '4G', 'centralizer': '48.f1.b1', 'counter': 20, 'group_counter': 1090131, 'group_order': 768, 'label': '4I', 'order': 4, 'powers': [8, 20], 'representative': 3441583254345367, 'size': 48}
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id: 110944311
{'aut_label': '4G', 'centralizer': '48.f1.b1', 'counter': 21, 'group_counter': 1090131, 'group_order': 768, 'label': '4J', 'order': 4, 'powers': [8, 21], 'representative': 4425408151401294, 'size': 48}
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id: 110944312
{'aut_label': '6A', 'centralizer': '128.a1.a1', 'counter': 22, 'group_counter': 1090131, 'group_order': 768, 'label': '6A', 'order': 6, 'powers': [11, 2], 'representative': 1283092253383009, 'size': 128}
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id: 110944313
{'aut_label': '8A', 'centralizer': '48.n1.a1', 'counter': 23, 'group_counter': 1090131, 'group_order': 768, 'label': '8A', 'order': 8, 'powers': [13, 23], 'representative': 2725414232668201, 'size': 48}
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id: 110944314
{'aut_label': '8A', 'centralizer': '48.n1.a1', 'counter': 24, 'group_counter': 1090131, 'group_order': 768, 'label': '8B', 'order': 8, 'powers': [13, 24], 'representative': 4930298537645568, 'size': 48}
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gps_qchar • Show schema
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id: 4799677
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
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id: 4799688
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1], 'schur_index': 1}
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id: 4799694
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, 1], 'schur_index': 1}
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id: 4799695
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
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id: 4799696
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, -1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, -1, 0, 0], 'schur_index': 1}
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id: 4799697
{'cdim': 2, 'counter': 6, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.2b', 'multiplicity': 1, 'nt': [6, 3], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -2, -2, 2, 2, 0, 0, -1, -2, 2, 0, 0, 2, -2, 0, 0, 0, 0, 1, 0, 0], 'schur_index': 1}
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id: 4799698
{'cdim': 3, 'counter': 7, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 1, 1, 0, 3, 3, 1, 1, -1, -1, -1, -1, -1, -1, 0, 1, 1], 'schur_index': 1}
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id: 4799699
{'cdim': 3, 'counter': 8, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, 3, -1, 3, 1, 1, 0, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 0, -1, -1], 'schur_index': 1}
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id: 4799700
{'cdim': 3, 'counter': 9, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, -1, 3, -1, 1, 1, 0, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 0, -1, -1], 'schur_index': 1}
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id: 4799678
{'cdim': 3, 'counter': 10, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, -1, -1, 0, 3, 3, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1], 'schur_index': 1}
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id: 4799679
{'cdim': 3, 'counter': 11, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, 3, -1, 3, -1, -1, 0, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 1, 1], 'schur_index': 1}
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id: 4799680
{'cdim': 3, 'counter': 12, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, -1, 3, -1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 1], 'schur_index': 1}
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id: 4799681
{'cdim': 3, 'counter': 13, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3g', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -3, 1, 3, -1, -1, 1, 0, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 0, -1, 1], 'schur_index': 1}
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id: 4799682
{'cdim': 3, 'counter': 14, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3h', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, -3, 1, 3, -1, 1, -1, 0, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 0, 1, -1], 'schur_index': 1}
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id: 4799683
{'cdim': 3, 'counter': 15, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3i', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 1, -3, -1, 3, -1, 1, 0, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 0, -1, 1], 'schur_index': 1}
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id: 4799684
{'cdim': 3, 'counter': 16, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3j', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 1, -3, -1, 3, 1, -1, 0, 1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 0, 1, -1], 'schur_index': 1}
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id: 4799685
{'cdim': 3, 'counter': 17, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3k', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 1, 1, -1, -1, -1, 1, 0, -3, 3, -1, 1, -1, 1, -1, 1, -1, 1, 0, 1, -1], 'schur_index': 1}
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id: 4799686
{'cdim': 3, 'counter': 18, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.3l', 'multiplicity': 1, 'nt': [6, 11], 'qdim': 3, 'qvalues': [3, -3, -3, 3, 1, 1, -1, -1, 1, -1, 0, -3, 3, 1, -1, -1, 1, 1, -1, 1, -1, 0, -1, 1], 'schur_index': 1}
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id: 4799687
{'cdim': 6, 'counter': 19, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, 0, 0, 0, -2, -2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4799689
{'cdim': 6, 'counter': 20, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.6b', 'multiplicity': 1, 'nt': [12, 100], 'qdim': 6, 'qvalues': [6, -6, -6, 6, 2, 2, -2, -2, 0, 0, 0, 2, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4799690
{'cdim': 12, 'counter': 21, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.12a', 'multiplicity': 1, 'nt': [16, 776], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 2, 2, 0, 0, 0, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4799691
{'cdim': 12, 'counter': 22, 'faithful': False, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.12b', 'multiplicity': 1, 'nt': [24, 985], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, -2, -2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4799692
{'cdim': 12, 'counter': 23, 'faithful': True, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.12c', 'multiplicity': 1, 'nt': [24, 1724], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, -2, 2, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4799693
{'cdim': 12, 'counter': 24, 'faithful': True, 'group': '768.1090131', 'group_order': 768, 'image': None, 'label': '768.1090131.12d', 'multiplicity': 1, 'nt': [24, 1724], 'qdim': 12, 'qvalues': [12, -12, 4, -4, 0, 0, 0, 0, 2, -2, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 7846136
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id: 7846147
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id: 7846153
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id: 7846154
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id: 7846155
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id: 7846156
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id: 7846157
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id: 7846158
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id: 7846159
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id: 7846137
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id: 7846138
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id: 7846139
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id: 7846140
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id: 7846141
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id: 7846142
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id: 7846143
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id: 7846144
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id: 7846145
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id: 7846146
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id: 7846148
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id: 7846149
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id: 7846150
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '768.1090131', 'group_counter': 1090131, 'group_order': 768, 'image': None, 'image_isoclass': '384.18135', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 2, 'label': '768.1090131.12b', 'nt': [24, 985], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 7846151
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '768.1090131', 'group_counter': 1090131, 'group_order': 768, 'image': None, 'image_isoclass': '768.1090131', 'image_order': 768, 'indicator': 1, 'kernel': '768.a1.a1', 'kernel_order': 1, 'label': '768.1090131.12c', 'nt': [24, 1724], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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id: 7846152
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 1, 'dim': 12, 'faithful': True, 'field': [0, 1], 'group': '768.1090131', 'group_counter': 1090131, 'group_order': 768, 'image': None, 'image_isoclass': '768.1090131', 'image_order': 768, 'indicator': 1, 'kernel': '768.a1.a1', 'kernel_order': 1, 'label': '768.1090131.12d', 'nt': [24, 1724], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
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gps_subgroup_search • Show schema
Hide schema
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id: 68521344
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 768, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '768.1090131.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1090131', 'subgroup_hash': 1090131, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5:S_4', 'supersolvable': False, 'sylow': 0}
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id: 68521455
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 384, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18231', 'subgroup_hash': 18231, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
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id: 68521566
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '768.1090131.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 68521677
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '768.1090131.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
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id: 68521788
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '768.1090131.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.26535', 'subgroup_hash': 26535, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5:D_4', 'supersolvable': True, 'sylow': 2}
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id: 68521828
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 192, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1023', 'subgroup_hash': 1023, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:A_4', 'supersolvable': False, 'sylow': 0}
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id: 68521839
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 68521850
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.4.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1538', 'subgroup_hash': 1538, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3:S_4', 'supersolvable': False, 'sylow': 0}
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id: 68521861
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.4.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.944', 'subgroup_hash': 944, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:D_6', 'supersolvable': False, 'sylow': 0}
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id: 68521345
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '128.2258', 'subgroup_hash': 2258, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 68521356
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1747', 'subgroup_hash': 1747, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 68521367
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.857', 'subgroup_hash': 857, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
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id: 68521378
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
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id: 68521389
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.1755', 'subgroup_hash': 1755, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4:D_4', 'supersolvable': True, 'sylow': 0}
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id: 68521400
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
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id: 68521411
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
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id: 68521422
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521433
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521444
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 19, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.f1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521456
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.f1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.f1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521467
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521478
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521489
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521500
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 64, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.6.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.931', 'subgroup_hash': 931, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521511
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521522
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521533
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 68521544
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 68521555
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521567
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521578
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521589
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.227', 'subgroup_hash': 227, 'subgroup_order': 96, 'subgroup_tex': 'C_2^2:S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521600
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 68521611
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.8.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.64', 'subgroup_hash': 64, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:S_3', 'supersolvable': False, 'sylow': 0}
-
id: 68521622
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521633
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521644
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521655
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.264', 'subgroup_hash': 264, 'subgroup_order': 64, 'subgroup_tex': 'D_4:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68521666
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521678
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521689
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521700
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521711
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521722
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521733
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521744
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521755
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521766
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.255', 'subgroup_hash': 255, 'subgroup_order': 64, 'subgroup_tex': 'Q_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521777
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.101', 'subgroup_hash': 101, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521789
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521800
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521811
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521821
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521822
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.m1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521823
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 55, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.m1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521824
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521825
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521826
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.n1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521827
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.n1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521829
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521830
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521831
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521832
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521833
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521834
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521835
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521836
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521837
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521838
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521841
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.136', 'subgroup_hash': 136, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521843
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521844
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521845
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521846
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521848
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521849
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.y1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.y1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.138', 'subgroup_hash': 138, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521851
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521852
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.z1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521854
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.12.z1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.z1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521856
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521857
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521858
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521859
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.b1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.48', 'subgroup_hash': 48, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521860
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521862
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521863
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 68521864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 68521865
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 93, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 68521866
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 94, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 68521867
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 95, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521868
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521870
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521871
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521346
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521347
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521348
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.40', 'subgroup_hash': 40, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\SD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521349
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.41', 'subgroup_hash': 41, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521350
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521351
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521352
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521353
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521354
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521355
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521357
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521358
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521359
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521360
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521361
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.48', 'subgroup_hash': 48, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521362
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521363
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521364
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521365
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521366
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521368
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521369
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521370
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.t1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521371
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.t1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521372
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521373
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521374
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521375
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521376
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521377
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521379
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521380
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521381
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521382
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521383
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521384
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521385
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521386
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521387
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521388
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521390
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521391
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521392
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521393
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521394
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521395
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521396
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521397
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521398
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521399
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521401
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521402
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521403
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521404
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521405
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521406
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521407
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521408
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521409
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bm1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521410
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bm1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bm1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521412
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521413
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521414
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bn1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521415
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bn1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bn1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521416
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521417
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.49', 'subgroup_hash': 49, 'subgroup_order': 32, 'subgroup_tex': 'D_4:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521418
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521419
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521420
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521421
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521423
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521424
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bs1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521425
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bs1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bs1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521426
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521427
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521428
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521429
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521430
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521431
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bv1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521432
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bv1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bv1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521434
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521435
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521436
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521437
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521438
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521439
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.by1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.by1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521440
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521441
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.44', 'subgroup_hash': 44, 'subgroup_order': 32, 'subgroup_tex': 'Q_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521442
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521443
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.24.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.11', 'subgroup_hash': 11, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521445
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521446
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521447
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521448
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521449
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521450
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521451
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.b2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521452
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521453
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521454
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521457
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521458
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521459
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521460
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521461
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521462
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521463
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.32.d1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.d1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.12', 'subgroup_hash': 12, 'subgroup_order': 24, 'subgroup_tex': 'S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521464
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 207, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': 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: 68521465
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 208, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': 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: 68521466
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 209, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.48', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 48, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521468
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521469
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521470
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521471
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521472
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521473
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521474
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521475
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521476
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521477
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521479
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521480
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521481
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521482
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521483
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521484
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521485
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521486
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521487
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521488
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521490
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521491
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521492
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521493
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.s1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521494
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521495
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.s1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521496
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521497
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.t1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521498
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521499
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.t1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521501
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521502
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521503
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521504
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521505
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u2.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u2.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521506
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.u2.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u2.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521507
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521508
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521509
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521510
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521512
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521513
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521514
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521515
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.z2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521516
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.z2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521517
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521518
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521519
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521520
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521521
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bc1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521523
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bc1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521524
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521525
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 262, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521526
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 263, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bd1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521527
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bd1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521528
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521529
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521530
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 267, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.be1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521531
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.be1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521532
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521534
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521535
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bf1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521536
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bf1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521537
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521538
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521539
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521540
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521541
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521542
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521543
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521545
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521546
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521547
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521548
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bk1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521549
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bk1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521550
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521551
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521552
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bl1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521553
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bl1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521554
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521556
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bm1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bm1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521557
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521558
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.8', 'subgroup_hash': 8, 'subgroup_order': 16, 'subgroup_tex': '\\SD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521559
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521560
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521561
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521562
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.9', 'subgroup_hash': 9, 'subgroup_order': 16, 'subgroup_tex': 'Q_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521563
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521564
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 298, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521565
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 299, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521568
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 300, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521569
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 301, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521570
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 302, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bs1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521571
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 303, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521572
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 304, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bt1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521573
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 305, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521574
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 306, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bu1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521575
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 307, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521576
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 308, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521577
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 309, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521579
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 310, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68521580
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 311, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521581
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 312, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.by1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.by1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521582
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 313, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bz1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521583
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 314, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bz1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521584
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 315, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bz1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521585
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 316, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.bz1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bz1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521586
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 317, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ca1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ca1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521587
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 318, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ca1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ca1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521588
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 319, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521590
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 320, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521591
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 321, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521592
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 322, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521593
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 323, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521594
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 324, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521595
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 325, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ce1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521596
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 326, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ce1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521597
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 327, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ce1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521598
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 328, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ce1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ce1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521599
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 329, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521601
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 330, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68521602
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 331, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ch1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ch1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521603
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 332, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ci1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ci1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521604
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 333, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ci1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ci1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.13', 'subgroup_hash': 13, 'subgroup_order': 16, 'subgroup_tex': 'D_4:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68521605
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 334, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521606
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 335, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.ck1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ck1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521607
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 336, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521608
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 337, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521609
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 338, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521610
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 339, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cn1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cn1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68521612
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 340, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.co1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.co1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521613
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 341, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.48.cp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.cp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521614
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 342, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 68521615
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 343, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521616
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 344, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521617
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 345, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521618
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 346, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521619
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 347, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521620
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 348, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521621
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 349, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.64.c2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 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': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68521623
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 350, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['S'], '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: 68521624
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 351, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521625
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 352, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521626
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 353, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521627
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 354, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.b2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521628
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 355, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521629
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 356, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521630
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 357, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521631
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 358, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521632
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 359, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521634
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 360, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521635
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 361, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521636
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 362, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521637
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 363, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521638
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 364, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521639
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 365, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521640
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 366, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521641
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 367, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521642
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 368, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.i2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521643
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 369, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521645
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 370, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521646
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 371, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521647
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 372, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521648
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 373, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521649
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 374, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521650
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 375, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521651
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 376, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521652
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 377, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521653
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 378, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.l2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521654
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 379, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521656
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 380, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521657
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 381, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.m2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521658
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 382, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.m2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521659
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 383, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521660
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 384, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521661
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 385, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521662
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 386, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521663
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 387, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521664
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 388, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521665
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 389, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521667
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 390, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521668
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 391, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521669
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 392, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521670
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 393, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521671
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 394, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521672
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 395, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521673
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 396, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521674
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 397, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521675
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 398, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521676
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 399, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521679
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 400, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521680
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 401, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.v2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521681
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 402, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.v2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521682
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 403, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521683
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 404, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521684
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 405, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521685
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 406, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521686
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 407, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.y1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521687
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 408, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.y1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521688
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 409, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521690
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 410, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521691
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 411, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.z1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521692
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 412, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.z1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521693
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 413, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521694
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 414, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521695
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 415, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.ba1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521696
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 416, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.ba1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521697
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 417, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521698
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 418, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521699
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 419, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bb1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521701
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 420, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bb1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521702
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 421, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521703
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 422, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521704
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 423, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521705
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 424, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521706
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 425, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521707
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 426, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521708
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 427, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521709
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 428, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521710
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 429, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521712
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 430, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521713
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 431, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521714
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 432, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521715
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 433, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521716
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 434, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521717
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 435, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521718
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 436, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521719
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 437, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521720
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 438, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521721
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 439, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bo1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bo1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 68521723
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 440, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521724
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 441, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bp1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bp1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521725
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 442, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521726
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 443, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bq1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bq1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521727
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 444, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521728
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 4, 'counter': 445, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.br1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.br1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521729
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 446, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521730
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 447, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521731
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 448, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521732
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 449, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521734
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 450, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521735
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 451, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521736
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 452, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521737
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 453, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521738
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 454, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521739
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 455, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521740
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 456, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521741
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 457, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bw1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bw1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521742
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 458, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521743
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 459, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521745
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 460, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521746
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 461, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521747
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 462, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521748
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 463, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.c2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.c2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521749
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 464, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521750
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 465, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.96.bx1.d2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bx1.d2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': 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: 68521751
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 466, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 68521752
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 467, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.128.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 68521753
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 468, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.128.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '128.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 68521754
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 469, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1090131.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1538', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1538, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'D3', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68521756
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 470, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521757
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 471, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521758
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 472, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521759
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 473, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521760
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 474, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521761
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 475, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521762
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 476, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.e2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521763
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 477, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.e2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521764
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 478, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521765
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 479, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521767
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 480, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521768
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 481, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521769
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 482, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.h2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521770
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 483, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.h2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521771
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 484, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521772
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 485, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521773
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 486, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521774
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 487, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.i2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521775
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 488, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521776
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 489, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521778
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 490, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521779
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 491, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521780
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 492, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521781
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 493, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521782
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 494, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521783
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 495, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521784
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 496, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521785
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 497, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521786
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 498, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521787
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 499, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521790
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 500, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521791
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 501, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521792
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 502, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521793
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 503, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.q2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.q2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521794
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 504, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521795
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 505, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521796
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 506, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.r1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.r1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521797
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 507, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.r1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.r1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521798
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 508, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521799
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 509, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521801
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 510, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.s1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.s1.c1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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: 68521802
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 511, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.192.s1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.s1.d1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521803
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 512, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521804
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 513, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521805
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 514, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521806
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 515, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521807
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 516, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521808
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 517, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1090131.192.t2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.t2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': 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}
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id: 68521809
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 518, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '768.1090131.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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id: 68521810
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 2, 'counter': 519, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '768.1090131.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '384.18135', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18135, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^2:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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id: 68521812
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 520, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521813
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 521, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521814
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 522, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521815
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 523, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521816
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 524, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521817
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 525, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521818
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 526, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521819
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 527, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1090131.384.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, '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}
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id: 68521820
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 1, 'counter': 528, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '768.1090131.768.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '768.1090131', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1090131, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5:S_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 68521638
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '48.i1.b1'], 'contains': ['192.c1.b1', '192.q1.b1', '192.t1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [940, -1, 2773, -1, 1036, -1, 6809, -1], 'generators': [1, 1558054095215088, 4934975208295326], 'label': '768.1090131.96.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '96.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
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id: 68521453
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '8.d1.d1', '8.e1.b1', '16.a1.a1'], 'contains': ['64.b1.a1', '96.br1.b1', '128.b1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [861, -1, 2472, -1, 846, -1, 7864, -1], 'generators': [84307934393430, 1822337812123926, 359890668365808, 85621839894847], 'label': '768.1090131.32.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.c1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 68521639
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.a1', '48.i1.a1', '48.s1.a1'], 'contains': ['192.c1.a1', '192.q2.a1', '192.t2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [659, -1, 564, -1, 946, -1, 8858, -1], 'generators': [312321447414, 1, 360320459007774], 'label': '768.1090131.96.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '96.i2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521640
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.a2', '48.i1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.q2.a2', '192.t2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [659, -1, 635, -1, 946, -1, 9019, -1], 'generators': [312321447414, 1, 461960891286], 'label': '768.1090131.96.i2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '96.i2.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521454
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.b1.a1'], 'contains': ['64.c2.a1', '96.bx1.a1', '128.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 64, -1, 452, -1, 9540, -1], 'generators': [84307934393430, 4047630492624, 359728823398326, 1821883084207920], 'label': '768.1090131.32.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.d1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521344
{'ambient': '768.1090131', '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': '384.a1.a1', 'complements': ['768.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1464, 3930, 986, 3052, 1397, 4302, 6278, 2827], 'generators': [84307934393430, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68521345
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 8, 'centralizer': '96.a1.a1', 'complements': ['128.b1.a1', '128.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.d1.a1', '12.g1.a1', '12.i1.a1', '12.i1.b1', '12.o1.a1', '12.o1.b1', '12.s1.a1', '12.t1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5063, 5601, 6580, 5509, 4362, 6108, 2784, 5173], 'generators': [1822337812123926, 312321447414, 359890668365808, 1, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521346
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.i1.a1', '48.bf1.a1', '48.bf1.b1', '48.bl1.a1', '48.bl1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1279, -1, 1860, -1, 1638, -1, 8022, -1], 'generators': [312321447414, 1821036378652951, 359890668365808, 461960891286, 1821036378652950], 'label': '768.1090131.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521347
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.e1.b1', '48.f1.b1', '48.i1.b1', '48.bf1.c1', '48.bf1.d1', '48.bl1.c1', '48.bl1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1279, -1, 3493, -1, 1638, -1, 5971, -1], 'generators': [1821036378652951, 359890668365808, 1821036378652950, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.f1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521348
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.k1.a1', '48.m1.a1', '48.n1.a1', '48.bm1.a1', '48.bm1.b1', '48.bn1.a1', '48.bn1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9950, -1, 9714, -1, 9235, -1, 294, -1], 'generators': [1558496692068486, 4047630492625, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521349
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.l1.a1', '48.m1.a1', '48.n1.a1', '48.bo1.a1', '48.bo1.b1', '48.bp1.a1', '48.bp1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9760, -1, 9979, -1, 9587, -1, 46, -1], 'generators': [1558496692068486, 1821036378652951, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521350
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.h1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '48.o1.a1', '48.p1.a1', '48.u1.a1', '48.u2.a1', '48.u2.b1', '48.bs1.a1', '48.bz1.a1', '48.bz1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2967, -1, 3738, -1, 5676, -1, 6319, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521351
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.c1.a1', '12.h1.b1'], 'contains': ['48.c1.b1', '48.d1.b1', '48.e1.b1', '48.o1.b1', '48.p1.a1', '48.u1.b1', '48.u2.c1', '48.u2.d1', '48.bs1.b1', '48.bz1.c1', '48.bz1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2967, -1, 5302, -1, 5676, -1, 5222, -1], 'generators': [1822337812123926, 4047630492625, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521352
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '12.i1.b1'], 'contains': ['48.o1.a1', '48.q1.a1', '48.r1.a1', '48.bt1.a1', '48.bu1.a1', '48.ca1.a1', '48.cb1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5144, -1, 7942, -1, 5386, -1, 2155, -1], 'generators': [1822337812123926, 312321447414, 3846697444535406, 359890668365808, 1], 'label': '768.1090131.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521353
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '12.i1.a1'], 'contains': ['48.o1.b1', '48.q1.a1', '48.r1.a1', '48.bt1.b1', '48.bu1.b1', '48.ca1.b1', '48.cb1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5144, -1, 8010, -1, 5386, -1, 1888, -1], 'generators': [1822337812123926, 359890668365808, 1, 1558328613944424, 3846242716609368], 'label': '768.1090131.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.j1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521354
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.i1.b1'], 'contains': ['48.o1.a1', '48.r1.a1', '48.bv1.a1', '48.cc1.a1', '48.cd1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3267, -1, 6261, -1, 3842, -1, 3952, -1], 'generators': [1822337812123926, 1179762397854126, 312321447414, 359890668365808, 1], 'label': '768.1090131.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521355
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.d1.a1', '12.i1.a1'], 'contains': ['48.o1.b1', '48.r1.a1', '48.bv1.b1', '48.cc1.b1', '48.cd1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3267, -1, 6910, -1, 3842, -1, 3136, -1], 'generators': [1558496692068486, 1822337812123926, 359890668365808, 1, 3846242716609368], 'label': '768.1090131.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.k1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521356
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530050', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.c1.a1', '12.f1.a1', '12.g1.a1', '12.j1.a1', '12.k1.a1', '12.p1.a1', '12.q1.a1', '12.u1.a1', '12.u1.b1', '12.v1.a1', '12.v1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8075, -1, 8025, -1, 7617, -1, 1763, -1], 'generators': [1558496692068486, 1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521357
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.a1', '12.h1.a1'], 'contains': ['48.f1.a1', '48.o1.a1', '48.v1.a1', '48.ce1.a1', '48.ce1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2122, -1, 2324, -1, 2679, -1, 7463, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.l1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521358
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.e1.b1', '12.h1.b1'], 'contains': ['48.f1.b1', '48.o1.b1', '48.v1.b1', '48.ce1.c1', '48.ce1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2122, -1, 3896, -1, 2679, -1, 5633, -1], 'generators': [3844916347312825, 1822337812123926, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.l1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521359
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.e1.a1', '12.e1.b1', '12.f1.a1', '12.g1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['48.g1.a1', '48.o1.a1', '48.o1.b1', '48.q1.a1', '48.w1.a1', '48.bq1.a1', '48.bq1.b1', '48.bx1.a1', '48.cf1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6849, -1, 6008, -1, 6219, -1, 3580, -1], 'generators': [1822337812123926, 359890668365808, 1, 461960891286, 3846242716609368], 'label': '768.1090131.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521360
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['48.h1.a1', '48.o1.a1', '48.o1.b1', '48.r1.a1', '48.x1.a1', '48.br1.a1', '48.br1.b1', '48.by1.a1', '48.cg1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3414, -1, 6664, -1, 2869, -1, 3762, -1], 'generators': [1822337812123926, 359890668365808, 1, 735925055088, 3846242716609368], 'label': '768.1090131.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521361
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.j1.a1', '48.k1.a1', '48.l1.a1', '48.p1.a1', '48.q1.a1', '48.z1.a1', '48.z2.a1', '48.z2.b1', '48.ch1.a1', '48.ci1.a1', '48.ci1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7596, -1, 7440, -1, 7999, -1, 1476, -1], 'generators': [1822337812123926, 4047630492625, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.o1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521362
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.g1.a1', '12.j1.a1'], 'contains': ['48.m1.a1', '48.q1.a1', '48.r1.a1', '48.ba1.a1', '48.cj1.a1', '48.cl1.a1', '48.cm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8204, -1, 9046, -1, 7573, -1, 1115, -1], 'generators': [1822337812123926, 1179762397854126, 3846541581724590, 359890668365808, 1], 'label': '768.1090131.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.p1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521363
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.n1.a1', '48.q1.a1', '48.bb1.a1', '48.cn1.a1', '48.cn1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8864, -1, 9536, -1, 8675, -1, 415, -1], 'generators': [1822337812123926, 359890668365808, 3845532940242606, 1179668884439070, 3845532940242607], 'label': '768.1090131.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521364
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.d1.a1'], 'contains': ['48.r1.a1', '48.co1.a1', '48.cp1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3698, -1, 8651, -1, 2299, -1, 2401, -1], 'generators': [1558496692068486, 1822337812123926, 3846541581724590, 359890668365808, 1], 'label': '768.1090131.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.r1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68521365
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['48.u1.a1', '48.u1.b1', '48.u2.b1', '48.u2.d1', '48.w1.a1', '48.z1.a1', '48.z2.b1', '48.bc1.b1', '48.bc1.d1', '48.bd1.a1', '48.bd1.c1', '48.bg1.b1', '48.bh1.a1', '48.bi1.a1', '48.bj1.b1'], 'core': '768.a1.a1', 'coset_action_label': '24T2176', 'count': 12, 'diagramx': [6966, -1, 5368, -1, 6665, -1, 4441, -1], 'generators': [4047630492625, 312321447414, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.s1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521366
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['48.u1.a1', '48.u1.b1', '48.u2.a1', '48.u2.c1', '48.w1.a1', '48.z1.a1', '48.z2.a1', '48.bc1.a1', '48.bc1.c1', '48.bd1.b1', '48.bd1.d1', '48.bg1.a1', '48.bh1.b1', '48.bi1.b1', '48.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': '24T2176', 'count': 12, 'diagramx': [6966, -1, 5128, -1, 6665, -1, 4379, -1], 'generators': [312321447414, 1821036378652951, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.s1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521367
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530058', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.e1.b1', '12.g1.a1', '12.w1.a1', '12.w1.b1', '12.x1.a1', '12.x1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7109, -1, 4975, -1, 6364, -1, 4552, -1], 'generators': [1558496692068486, 359890668365808, 1822337812123926, 4415227175928, 4415227175929, 1179562541714328, 312321447414], 'label': '768.1090131.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521368
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.u2.a1', '48.v1.a1', '48.y1.a1', '48.be1.a1', '48.bf1.b1', '48.bk1.a1', '48.bl1.b1'], 'core': '768.a1.a1', 'coset_action_label': '24T1724', 'count': 12, 'diagramx': [1434, -1, 1793, -1, 1837, -1, 8217, -1], 'generators': [312321447414, 1821036378652951, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.t1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521369
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.u2.b1', '48.v1.a1', '48.y1.a1', '48.be1.b1', '48.bf1.a1', '48.bk1.b1', '48.bl1.a1'], 'core': '768.a1.a1', 'coset_action_label': '24T1724', 'count': 12, 'diagramx': [1434, -1, 1941, -1, 1837, -1, 8121, -1], 'generators': [4047630492625, 312321447414, 359890668365808, 461960891286, 1821036378652950], 'label': '768.1090131.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.t1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521370
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.u2.c1', '48.v1.b1', '48.y1.b1', '48.be1.c1', '48.bf1.d1', '48.bk1.c1', '48.bl1.d1'], 'core': '768.a1.a1', 'coset_action_label': '24T1724', 'count': 12, 'diagramx': [1434, -1, 3358, -1, 1837, -1, 6070, -1], 'generators': [1821036378652951, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.t1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.t1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521371
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.u2.d1', '48.v1.b1', '48.y1.b1', '48.be1.d1', '48.bf1.c1', '48.bk1.d1', '48.bl1.c1'], 'core': '768.a1.a1', 'coset_action_label': '24T1724', 'count': 12, 'diagramx': [1434, -1, 3424, -1, 1837, -1, 6166, -1], 'generators': [4047630492625, 359890668365808, 1821036378652950, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.t1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.t1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521372
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.z2.a1', '48.ba1.a1', '48.bb1.a1', '48.bm1.a1', '48.bn1.a1', '48.bo1.b1', '48.bp1.b1'], 'core': '768.a1.a1', 'coset_action_label': '24T2175', 'count': 12, 'diagramx': [9586, -1, 9785, -1, 9427, -1, 127, -1], 'generators': [1558496692068486, 1821036378652951, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.u1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521373
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.z2.b1', '48.ba1.a1', '48.bb1.a1', '48.bm1.b1', '48.bn1.b1', '48.bo1.a1', '48.bp1.a1'], 'core': '768.a1.a1', 'coset_action_label': '24T2175', 'count': 12, 'diagramx': [9586, -1, 9840, -1, 9427, -1, 198, -1], 'generators': [1558496692068486, 4047630492625, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.24.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.u1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521374
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.l1.a1', '12.r1.a1'], 'contains': ['48.bc1.a1', '48.bc1.b1', '48.bd1.a1', '48.bd1.b1', '48.bq1.a1', '48.bs1.a1', '48.bz1.c1', '48.bz1.d1', '48.ch1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3813, -1, 5169, -1, 5825, -1, 4226, -1], 'generators': [1822337812123926, 4253081604151, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.v1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521375
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.l1.b1', '12.r1.b1'], 'contains': ['48.bc1.c1', '48.bc1.d1', '48.bd1.c1', '48.bd1.d1', '48.bq1.b1', '48.bs1.b1', '48.bz1.a1', '48.bz1.b1', '48.ch1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3813, -1, 5211, -1, 5825, -1, 4627, -1], 'generators': [1822337812123926, 312321447414, 1183459680839575, 4047630492624, 359890668365808], 'label': '768.1090131.24.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.v1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521376
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.o1.a1', '12.s1.a1'], 'contains': ['48.br1.a1', '48.bt1.a1', '48.bv1.a1', '48.ca1.b1', '48.cc1.b1', '48.cj1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4971, -1, 7695, -1, 3996, -1, 2333, -1], 'generators': [1558496692068486, 1822337812123926, 312321447415, 359890668365808, 3846242716609368], 'label': '768.1090131.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.w1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521377
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.o1.b1', '12.s1.a1'], 'contains': ['48.br1.b1', '48.bt1.b1', '48.bv1.b1', '48.ca1.a1', '48.cc1.a1', '48.cj1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4971, -1, 7502, -1, 3996, -1, 2282, -1], 'generators': [1822337812123926, 1179762397854126, 312321447414, 359890668365808, 1558496692068487], 'label': '768.1090131.24.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.w1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521378
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.b1', '12.c1.a1', '12.e1.b1', '12.h1.b1', '12.i1.a1', '12.l1.a1', '12.m1.c1', '12.m1.d1', '12.r1.a1', '12.y1.a1', '12.y1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3731, -1, 5207, -1, 5097, -1, 4883, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521379
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.l1.a1', '12.r1.a1'], 'contains': ['48.bq1.a1', '48.ce1.c1', '48.ce1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2658, -1, 4725, -1, 4906, -1, 5359, -1], 'generators': [1822337812123926, 359890668365808, 3844916347312824, 1179562541714328, 3845190266530591], 'label': '768.1090131.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.x1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521380
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.l1.b1', '12.r1.b1'], 'contains': ['48.bq1.b1', '48.ce1.a1', '48.ce1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2658, -1, 2752, -1, 4906, -1, 7026, -1], 'generators': [1822337812123926, 312321447414, 1183672005485785, 359890668365808, 4415227175928], 'label': '768.1090131.24.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.x1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521381
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.s1.a1'], 'contains': ['48.bq1.a1', '48.bt1.a1', '48.bu1.a1', '48.ca1.b1', '48.cb1.b1', '48.cj1.a1', '48.ck1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6030, -1, 8095, -1, 5539, -1, 1547, -1], 'generators': [1822337812123926, 461960891287, 359890668365808, 1558328613944424, 3846242716609368], 'label': '768.1090131.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521382
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.b1', '12.s1.a1'], 'contains': ['48.bq1.b1', '48.bt1.b1', '48.bu1.b1', '48.ca1.a1', '48.cb1.a1', '48.cj1.a1', '48.ck1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6030, -1, 7886, -1, 5539, -1, 1598, -1], 'generators': [1822337812123926, 312321447414, 3846697444535406, 359890668365808, 1558496692068487], 'label': '768.1090131.24.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.y1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521383
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.o1.a1', '12.t1.a1'], 'contains': ['48.br1.a1', '48.bu1.a1', '48.bv1.a1', '48.cb1.b1', '48.cd1.b1', '48.cm1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5547, -1, 8062, -1, 4793, -1, 1965, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 1558328613944424, 3846242716609368], 'label': '768.1090131.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521384
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.o1.b1', '12.t1.a1'], 'contains': ['48.br1.b1', '48.bu1.b1', '48.bv1.b1', '48.cb1.a1', '48.cd1.a1', '48.cm1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5547, -1, 7852, -1, 4793, -1, 2016, -1], 'generators': [1822337812123926, 312321447414, 3846697444535406, 359890668365808, 1558054095215089], 'label': '768.1090131.24.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.z1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521385
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.l1.a1', '12.o1.a1'], 'contains': ['48.a1.b1', '48.bq1.a1', '48.br1.a1', '48.ca1.b1', '48.cd1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3556, -1, 6422, -1, 4142, -1, 3331, -1], 'generators': [1822337812123926, 461960891287, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521386
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.l1.b1', '12.o1.b1'], 'contains': ['48.a1.a1', '48.bq1.b1', '48.br1.b1', '48.ca1.a1', '48.cd1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3556, -1, 6068, -1, 4142, -1, 4051, -1], 'generators': [1822337812123926, 312321447414, 3846242716609369, 359890668365808, 461960891286], 'label': '768.1090131.24.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.ba1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521387
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.m1.a1', '12.r1.b1'], 'contains': ['48.be1.a1', '48.bf1.a1', '48.bw1.a1', '48.bz1.a1', '48.ce1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1967, -1, 2259, -1, 2481, -1, 7364, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bb1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521388
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1', '12.m1.b1', '12.r1.b1'], 'contains': ['48.be1.b1', '48.bf1.b1', '48.bw1.a1', '48.bz1.b1', '48.ce1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1967, -1, 2391, -1, 2481, -1, 7268, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.24.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bb1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521556
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.u1.b1', '24.by1.b1'], 'contains': ['96.bi1.b1', '96.bm1.a1', '96.bo1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9591, -1, 9582, -1, 9653, -1, 509, -1], 'generators': [1179762397854126, 3846541581724590, 795533260057254, 85621839894847], 'label': '768.1090131.48.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bm1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521389
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.c1.a1', '12.e1.a1', '12.h1.a1', '12.i1.b1', '12.l1.b1', '12.m1.a1', '12.m1.b1', '12.r1.b1', '12.y1.c1', '12.y1.d1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3731, -1, 4552, -1, 5097, -1, 5661, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521390
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.m1.c1', '12.r1.a1'], 'contains': ['48.be1.c1', '48.bf1.c1', '48.bw1.b1', '48.bz1.c1', '48.ce1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1967, -1, 4186, -1, 2481, -1, 5533, -1], 'generators': [3844916347312825, 1822337812123926, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.bb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bb1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521391
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1', '12.m1.d1', '12.r1.a1'], 'contains': ['48.be1.d1', '48.bf1.d1', '48.bw1.b1', '48.bz1.d1', '48.ce1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1967, -1, 4052, -1, 2481, -1, 5438, -1], 'generators': [1822337812123926, 4047630492625, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.24.bb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bb1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521392
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.o1.a1', '12.s1.a1'], 'contains': ['48.bq1.a1', '48.br1.a1', '48.bt1.a1', '48.bv1.a1', '48.bw1.a1', '48.ca1.a1', '48.cg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4313, -1, 6603, -1, 3443, -1, 2879, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 735925055088, 3846242716609368], 'label': '768.1090131.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521393
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.o1.b1', '12.s1.a1'], 'contains': ['48.bq1.b1', '48.br1.b1', '48.bt1.b1', '48.bv1.b1', '48.bw1.b1', '48.ca1.b1', '48.cg1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4313, -1, 6844, -1, 3443, -1, 2784, -1], 'generators': [1822337812123926, 359890668365808, 735925055088, 3846242716609368, 1558054095215089], 'label': '768.1090131.24.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bc1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521394
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.m1.a1', '12.m1.b1', '12.n1.a1', '12.n1.b1', '12.o1.a1', '12.t1.a1'], 'contains': ['48.br1.a1', '48.bu1.a1', '48.bw1.a1', '48.cd1.a1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5758, -1, 5946, -1, 5188, -1, 3853, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 461960891286, 3846242716609368], 'label': '768.1090131.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521395
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.c1', '12.m1.d1', '12.n1.c1', '12.n1.d1', '12.o1.b1', '12.t1.a1'], 'contains': ['48.br1.b1', '48.bu1.b1', '48.bw1.b1', '48.cd1.b1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5758, -1, 6485, -1, 5188, -1, 3037, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 3846242716609368, 1558054095215089], 'label': '768.1090131.24.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521396
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.bg1.a1', '48.bg1.b1', '48.bh1.a1', '48.bh1.b1', '48.bs1.a1', '48.bs1.b1', '48.bx1.a1', '48.ci1.a1', '48.ci1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8088, -1, 6778, -1, 7845, -1, 2958, -1], 'generators': [1822337812123926, 797114890868809, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.be1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521397
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.s1.a1'], 'contains': ['48.bt1.a1', '48.bt1.b1', '48.bv1.a1', '48.bv1.b1', '48.by1.a1', '48.cj1.a1', '48.cp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4801, -1, 7819, -1, 3006, -1, 2232, -1], 'generators': [1558496692068486, 1822337812123926, 312321447415, 3846541581724590, 359890668365808], 'label': '768.1090131.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bf1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521398
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.p1.a1', '12.s1.a1'], 'contains': ['48.bt1.a1', '48.bt1.b1', '48.bx1.a1', '48.ck1.a1', '48.cl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7921, -1, 8133, -1, 7061, -1, 1405, -1], 'generators': [1822337812123926, 735925055089, 1179762397854126, 3846541581724590, 359890668365808], 'label': '768.1090131.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521399
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.bu1.a1', '48.bu1.b1', '48.bv1.a1', '48.bv1.b1', '48.by1.a1', '48.cl1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5644, -1, 8175, -1, 3689, -1, 1648, -1], 'generators': [1822337812123926, 312321447415, 1179762397854126, 3846541581724590, 359890668365808], 'label': '768.1090131.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bh1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521400
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.i1.a1', '12.n1.c1', '12.n1.d1', '12.z1.a1', '12.z1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6627, -1, 6359, -1, 5948, -1, 3118, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 359890668365808, 4415227175928, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521401
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.p1.a1', '12.q1.a1'], 'contains': ['48.bx1.a1', '48.cn1.a1', '48.cn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9008, -1, 9207, -1, 8487, -1, 789, -1], 'generators': [1822337812123926, 3845383540000609, 359890668365808, 3845532940242606, 1179668884439070], 'label': '768.1090131.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bi1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521402
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.q1.a1', '12.t1.a1'], 'contains': ['48.b1.a1', '48.bu1.a1', '48.bu1.b1', '48.bx1.a1', '48.cm1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7999, -1, 8816, -1, 7263, -1, 1354, -1], 'generators': [1822337812123926, 461960891287, 3846697444535406, 359890668365808, 1179668884439070], 'label': '768.1090131.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bj1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521403
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.r1.a1', '12.s1.a1'], 'contains': ['48.bq1.a1', '48.bt1.b1', '48.bw1.b1', '48.by1.a1', '48.cc1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3112, -1, 6725, -1, 3252, -1, 3236, -1], 'generators': [1558496692068486, 1822337812123926, 461960891287, 359890668365808, 3846242716609368], 'label': '768.1090131.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bk1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521404
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.r1.b1', '12.s1.a1'], 'contains': ['48.bq1.b1', '48.bt1.a1', '48.bw1.a1', '48.by1.a1', '48.cc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3112, -1, 6196, -1, 3252, -1, 3671, -1], 'generators': [1822337812123926, 1179762397854126, 461960891287, 312321447414, 359890668365808], 'label': '768.1090131.24.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bk1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521405
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.br1.a1', '48.bu1.b1', '48.bv1.b1', '48.bw1.b1', '48.bx1.a1', '48.by1.a1', '48.cb1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4679, -1, 7130, -1, 4523, -1, 2492, -1], 'generators': [1822337812123926, 735925055089, 359890668365808, 1558328613944424, 3846242716609368], 'label': '768.1090131.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bl1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521406
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.s1.a1', '12.t1.a1'], 'contains': ['48.br1.b1', '48.bu1.a1', '48.bv1.a1', '48.bw1.a1', '48.bx1.a1', '48.by1.a1', '48.cb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4679, -1, 7204, -1, 4523, -1, 2587, -1], 'generators': [1822337812123926, 461960891287, 312321447414, 3846697444535406, 359890668365808], 'label': '768.1090131.24.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bl1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521407
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.r1.b1', '12.y1.c1'], 'contains': ['48.bz1.a1', '48.cc1.a1', '48.ce1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 3181, -1, 4681, -1, 6518, -1], 'generators': [1822337812123926, 1179762397854126, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.24.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bm1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521408
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.r1.b1', '12.y1.d1'], 'contains': ['48.bz1.b1', '48.cc1.a1', '48.ce1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 3264, -1, 4681, -1, 6580, -1], 'generators': [1558496692068486, 1822337812123926, 1558428122581230, 359890668365808, 85621839894847], 'label': '768.1090131.24.bm1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bm1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521409
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.r1.a1', '12.y1.a1'], 'contains': ['48.bz1.c1', '48.cc1.b1', '48.ce1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 5004, -1, 4681, -1, 5086, -1], 'generators': [1822337812123926, 4047630492624, 1558428122581230, 359890668365808, 1179562541714328], 'label': '768.1090131.24.bm1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bm1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521410
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.r1.a1', '12.y1.b1'], 'contains': ['48.bz1.d1', '48.cc1.b1', '48.ce1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2755, -1, 4808, -1, 4681, -1, 5297, -1], 'generators': [1822337812123926, 3846884234706384, 359890668365808, 1558054095215088, 85621839894847], 'label': '768.1090131.24.bm1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bm1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bm1.d1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521411
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.b1', '12.f1.a1', '12.i1.b1', '12.n1.a1', '12.n1.b1', '12.z1.c1', '12.z1.d1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6627, -1, 5914, -1, 5948, -1, 3692, -1], 'generators': [1822337812123926, 1562082513025344, 1562082513025345, 312321447414, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521412
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.l1.b1', '12.m1.a1'], 'contains': ['48.bz1.a1', '48.cd1.a1', '48.ce1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2852, -1, 3222, -1, 5030, -1, 6456, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 1183672005485785, 359890668365808], 'label': '768.1090131.24.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bn1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521413
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.l1.b1', '12.m1.b1'], 'contains': ['48.bz1.b1', '48.cd1.a1', '48.ce1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2852, -1, 3305, -1, 5030, -1, 6394, -1], 'generators': [1822337812123926, 312321447414, 1183459680839575, 359890668365808, 4415227175928], 'label': '768.1090131.24.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bn1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521414
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.l1.a1', '12.m1.c1'], 'contains': ['48.bz1.c1', '48.cd1.b1', '48.ce1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2852, -1, 5252, -1, 5030, -1, 5148, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808, 1179562541714328, 3845190266530591], 'label': '768.1090131.24.bn1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bn1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.c1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521415
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.l1.a1', '12.m1.d1'], 'contains': ['48.bz1.d1', '48.cd1.b1', '48.ce1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2852, -1, 5045, -1, 5030, -1, 4900, -1], 'generators': [1822337812123926, 4253081604151, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.24.bn1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bn1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bn1.d1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521416
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1', '12.m1.c1', '12.u1.a1', '12.v1.a1', '12.y1.a1', '12.y1.c1'], 'contains': ['48.bi1.a1', '48.bj1.a1', '48.bz1.a1', '48.bz1.c1', '48.cf1.a1', '48.ci1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7171, -1, 5087, -1, 6541, -1, 4503, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521417
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bo1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.b1', '12.m1.d1', '12.u1.b1', '12.v1.b1', '12.y1.b1', '12.y1.d1'], 'contains': ['48.bi1.b1', '48.bj1.b1', '48.bz1.b1', '48.bz1.d1', '48.cf1.a1', '48.ci1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7171, -1, 4949, -1, 6541, -1, 4565, -1], 'generators': [1822337812123926, 359890668365808, 1558054095215088, 735925055088, 85621839894847], 'label': '768.1090131.24.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bo1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521418
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.o1.a1', '12.o1.b1'], 'contains': ['48.ca1.a1', '48.ca1.b1', '48.cd1.a1', '48.cd1.b1', '48.cg1.a1', '48.cj1.a1', '48.co1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5397, -1, 7360, -1, 3588, -1, 2660, -1], 'generators': [1822337812123926, 359890668365808, 1558428122581231, 735925055088, 3846242716609368], 'label': '768.1090131.24.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bp1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521419
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.o1.a1', '12.o1.b1', '12.u1.a1', '12.u1.b1', '12.w1.a1', '12.w1.b1'], 'contains': ['48.ca1.a1', '48.ca1.b1', '48.cf1.a1', '48.ck1.a1', '48.cm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7707, -1, 7570, -1, 7162, -1, 1761, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 1558428122581231, 3846242716609368], 'label': '768.1090131.24.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bq1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521420
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.d1.a1', '12.s1.a1'], 'contains': ['48.cb1.a1', '48.cb1.b1', '48.cc1.a1', '48.cc1.b1', '48.cg1.a1', '48.cl1.a1', '48.cp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4565, -1, 7535, -1, 3106, -1, 2711, -1], 'generators': [1558496692068486, 1822337812123926, 312321447414, 359890668365808, 3846242716609368], 'label': '768.1090131.24.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.br1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521421
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.m1.a1', '12.n1.c1', '12.w1.a1', '12.x1.a1', '12.y1.d1', '12.z1.a1'], 'contains': ['48.ce1.a1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 4586, -1, 5994, -1, 5024, -1], 'generators': [1822337812123926, 86101381384801, 359890668365808, 1558054095215088, 735925055088], 'label': '768.1090131.24.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521422
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.a1', '12.n1.b1', '12.o1.a1', '12.u1.a1', '12.w1.a1', '12.y1.a1', '12.z1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6785, -1, 5842, -1, 5746, -1, 3799, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521423
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.m1.b1', '12.n1.d1', '12.w1.b1', '12.x1.b1', '12.y1.c1', '12.z1.b1'], 'contains': ['48.ce1.b1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 4683, -1, 5994, -1, 4962, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 4415227175928, 1179562541714328], 'label': '768.1090131.24.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521424
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.m1.c1', '12.n1.a1', '12.w1.b1', '12.x1.a1', '12.y1.b1', '12.z1.c1'], 'contains': ['48.ce1.c1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 4767, -1, 5994, -1, 4838, -1], 'generators': [1822337812123926, 3824964916138807, 359890668365808, 1558054095215088, 735925055088], 'label': '768.1090131.24.bs1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521425
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.m1.d1', '12.n1.b1', '12.w1.a1', '12.x1.b1', '12.y1.a1', '12.z1.d1'], 'contains': ['48.ce1.d1', '48.cf1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7063, -1, 4850, -1, 5994, -1, 4776, -1], 'generators': [1822337812123926, 1562082513025344, 312321447414, 359890668365808, 1179562541714328], 'label': '768.1090131.24.bs1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bs1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bs1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521426
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.n1.b1', '12.n1.d1', '12.u1.a1', '12.v1.b1', '12.z1.a1', '12.z1.c1'], 'contains': ['48.cf1.a1', '48.cn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8321, -1, 7258, -1, 7722, -1, 1705, -1], 'generators': [1822337812123926, 359890668365808, 3825182759822761, 1558054095215088, 735925055088], 'label': '768.1090131.24.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bt1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521427
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.928', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.n1.a1', '12.n1.c1', '12.u1.b1', '12.v1.a1', '12.z1.b1', '12.z1.d1'], 'contains': ['48.cf1.a1', '48.cn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8321, -1, 7299, -1, 7722, -1, 2072, -1], 'generators': [1822337812123926, 312321447414, 1562469074861448, 359890668365808, 1179562541714328], 'label': '768.1090131.24.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bt1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521428
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bu1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.t1.a1', '12.v1.a1', '12.v1.b1', '12.x1.a1', '12.x1.b1'], 'contains': ['48.b1.a1', '48.cb1.a1', '48.cb1.b1', '48.cf1.a1', '48.cl1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7272, -1, 8208, -1, 6960, -1, 1812, -1], 'generators': [1822337812123926, 1558428122581230, 359890668365808, 461960891286, 3846242716609368], 'label': '768.1090131.24.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bu1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521429
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '12.h1.a1', '12.l1.b1', '12.y1.c1'], 'contains': ['48.a1.a1', '48.bk1.a1', '48.bl1.a1', '48.bz1.a1', '48.ce1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1749, -1, 2151, -1, 2117, -1, 7628, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.24.bv1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bv1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521430
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '12.h1.a1', '12.l1.b1', '12.y1.d1'], 'contains': ['48.a1.a1', '48.bk1.b1', '48.bl1.b1', '48.bz1.b1', '48.ce1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1749, -1, 2087, -1, 2117, -1, 7724, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 85621839894847], 'label': '768.1090131.24.bv1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.bv1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521431
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '12.h1.b1', '12.l1.a1', '12.y1.a1'], 'contains': ['48.a1.b1', '48.bk1.c1', '48.bl1.c1', '48.bz1.c1', '48.ce1.d1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1749, -1, 3798, -1, 2117, -1, 5777, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.bv1.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bv1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521432
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bv1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '12.h1.b1', '12.l1.a1', '12.y1.b1'], 'contains': ['48.a1.b1', '48.bk1.d1', '48.bl1.d1', '48.bz1.d1', '48.ce1.c1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1749, -1, 3677, -1, 2117, -1, 5872, -1], 'generators': [1822337812123926, 359890668365808, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.24.bv1.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.bv1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bv1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521433
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.b1', '12.n1.a1', '12.o1.a1', '12.u1.b1', '12.w1.b1', '12.y1.b1', '12.z1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6785, -1, 5772, -1, 5746, -1, 4075, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 359890668365808, 4415227175928, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521434
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.i1.a1', '12.o1.a1', '12.y1.a1', '12.y1.b1', '12.z1.a1', '12.z1.b1'], 'contains': ['48.a1.b1', '48.cb1.b1', '48.cc1.b1', '48.cf1.a1', '48.cg1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4165, -1, 6132, -1, 4332, -1, 3489, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bw1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521435
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.i1.b1', '12.o1.b1', '12.y1.c1', '12.y1.d1', '12.z1.c1', '12.z1.d1'], 'contains': ['48.a1.a1', '48.cb1.a1', '48.cc1.a1', '48.cf1.a1', '48.cg1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4165, -1, 5883, -1, 4332, -1, 4147, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 3846242716609368], 'label': '768.1090131.24.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bw1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521436
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.p1.a1', '12.u1.a1'], 'contains': ['48.ci1.a1', '48.ck1.a1', '48.cn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8678, -1, 8988, -1, 8342, -1, 862, -1], 'generators': [1822337812123926, 4047630492624, 3845383540000609, 359890668365808, 1179668884439070], 'label': '768.1090131.24.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bx1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521437
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.bx1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.k1.a1', '12.p1.a1', '12.u1.b1'], 'contains': ['48.ci1.b1', '48.ck1.a1', '48.cn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8678, -1, 8933, -1, 8342, -1, 946, -1], 'generators': [1822337812123926, 797114890868809, 359890668365808, 3845532940242606, 1179668884439070], 'label': '768.1090131.24.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bx1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521438
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.p1.a1', '12.v1.a1'], 'contains': ['48.bm1.a1', '48.bo1.a1', '48.ci1.a1', '48.cl1.a1', '48.cn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9248, -1, 9260, -1, 8867, -1, 723, -1], 'generators': [1558496692068486, 1822337812123926, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.24.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.by1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521439
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.by1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.p1.a1', '12.v1.b1'], 'contains': ['48.bm1.b1', '48.bo1.b1', '48.ci1.b1', '48.cl1.a1', '48.cn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9248, -1, 9361, -1, 8867, -1, 652, -1], 'generators': [1822337812123926, 1179762397854126, 3846541581724590, 359890668365808, 85621839894847], 'label': '768.1090131.24.by1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.by1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.by1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521440
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.q1.a1', '12.u1.a1'], 'contains': ['48.bn1.a1', '48.bp1.a1', '48.ci1.a1', '48.cm1.a1', '48.cn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9368, -1, 9424, -1, 9008, -1, 511, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808, 1179668884439070, 3845532940242607], 'label': '768.1090131.24.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bz1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521441
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.bz1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.226', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1', '12.q1.a1', '12.u1.b1'], 'contains': ['48.bn1.b1', '48.bp1.b1', '48.ci1.b1', '48.cm1.a1', '48.cn1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9368, -1, 9471, -1, 9008, -1, 581, -1], 'generators': [1822337812123926, 4047630492625, 359890668365808, 3845532940242606, 1179668884439070], 'label': '768.1090131.24.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.bz1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521442
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.a1', '12.k1.a1', '12.q1.a1', '12.v1.a1'], 'contains': ['48.b1.a1', '48.ci1.a1', '48.cn1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8534, -1, 9102, -1, 8174, -1, 1201, -1], 'generators': [1822337812123926, 3846697444535406, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.24.ca1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.ca1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521443
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.e1.b1', '12.k1.a1', '12.q1.a1', '12.v1.b1'], 'contains': ['48.b1.a1', '48.ci1.b1', '48.cn1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8534, -1, 9159, -1, 8174, -1, 1030, -1], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1179668884439070, 85621839894847], 'label': '768.1090131.24.ca1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.ca1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ca1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521444
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.c1', '12.n1.d1', '12.o1.b1', '12.u1.a1', '12.w1.b1', '12.y1.c1', '12.z1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6785, -1, 5700, -1, 5746, -1, 4182, -1], 'generators': [1822337812123926, 1562082513025345, 312321447414, 4047630492624, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.6.f1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521445
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '16.a1.a1'], 'contains': ['64.b1.a1', '96.a1.a1', '128.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [597, -1, 2553, -1, 607, -1, 7767, -1], 'generators': [84307934393430, 1822337812123926, 84307934393431, 359890668365808], 'label': '768.1090131.32.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521446
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['64.c1.a1', '96.i1.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [165, -1, 314, -1, 64, -1, 9799, -1], 'generators': [84307934393430, 84307934393431, 1822038947023848, 795203061792528], 'label': '768.1090131.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.a1', 'old_label': '32.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68521447
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1'], 'contains': ['64.c1.b1', '96.i1.b1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [165, -1, 760, -1, 64, -1, 8554, -1], 'generators': [84307934393430, 2587548203909304, 84307934393431, 5621224034334630], 'label': '768.1090131.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.b1', 'old_label': '32.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68521448
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1'], 'contains': ['64.c2.a1', '96.i2.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [50, -1, 21, -1, 255, -1, 9872, -1], 'generators': [84307934393430, 84307934393431, 359728823398326, 1821883084207920], 'label': '768.1090131.32.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.b2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521449
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a2'], 'contains': ['64.c2.a2', '96.i2.a2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [50, -1, 163, -1, 255, -1, 9968, -1], 'generators': [84307934393430, 84307934393431, 312321447414, 461960891286], 'label': '768.1090131.32.b2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '32.b2.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521450
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '16.b1.b1'], 'contains': ['64.c2.b1', '96.i2.b1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [50, -1, 502, -1, 255, -1, 8887, -1], 'generators': [84307934393430, 84307934393431, 3437629559701230, 4934975208295326], 'label': '768.1090131.32.b2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.b2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521451
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '16.b1.b2'], 'contains': ['64.c2.b2', '96.i2.b2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [50, -1, 619, -1, 255, -1, 9040, -1], 'generators': [84307934393430, 84307934393431, 1558054095215088, 3846242716609368], 'label': '768.1090131.32.b2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '32.b2.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521452
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '32.c1', 'aut_quo_index': None, 'aut_stab_index': 32, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '8.d1.c1', '8.e1.a1', '16.a1.a1'], 'contains': ['64.b1.a1', '96.br1.a1', '128.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [861, -1, 2513, -1, 846, -1, 7825, -1], 'generators': [84307934393430, 1822337812123926, 4047630492624, 359890668365808], 'label': '768.1090131.32.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.c1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.c1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521455
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['384.f1.a1', '384.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1318, 5601, 5290, 5509, 1257, 5803, 6208, 5102], 'generators': [84307934393430, 1822337812123926, 84307934393431, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68521456
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.d1', '12.n1.c1', '12.o1.b1', '12.u1.b1', '12.w1.a1', '12.y1.d1', '12.z1.d1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6785, -1, 5629, -1, 5746, -1, 3906, -1], 'generators': [1822337812123926, 1562082513025344, 4047630492625, 312321447414, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.6.f1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.f1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.f1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521457
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.a1', '16.b1.a2'], 'contains': ['64.c2.a2', '96.bx1.a2', '128.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 125, -1, 452, -1, 9621, -1], 'generators': [84307934393430, 312321447414, 4047630492624, 461960891286], 'label': '768.1090131.32.d1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '32.d1.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521458
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '16.b1.a1'], 'contains': ['64.c2.a1', '96.bx1.b1', '128.b1.b1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 229, -1, 452, -1, 9661, -1], 'generators': [84307934393430, 359728823398326, 85621839894847, 1821883084207920], 'label': '768.1090131.32.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.d1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521459
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.b1', '16.b1.a2'], 'contains': ['64.c2.a2', '96.bx1.b2', '128.b1.b1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 275, -1, 452, -1, 9700, -1], 'generators': [84307934393430, 312321447414, 461960891286, 85621839894847], 'label': '768.1090131.32.d1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '32.d1.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521460
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '16.b1.b1'], 'contains': ['64.c2.b1', '96.bx1.c1', '128.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 465, -1, 452, -1, 8944, -1], 'generators': [84307934393430, 4047630492624, 3437629559701230, 4934975208295326], 'label': '768.1090131.32.d1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.d1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.c1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521461
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.c1', '16.b1.b2'], 'contains': ['64.c2.b2', '96.bx1.c2', '128.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 581, -1, 452, -1, 9098, -1], 'generators': [84307934393430, 4047630492624, 1558054095215088, 3846242716609368], 'label': '768.1090131.32.d1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '32.d1.c2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.c2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521462
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '16.b1.b1'], 'contains': ['64.c2.b1', '96.bx1.d1', '128.b1.b1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 438, -1, 452, -1, 8984, -1], 'generators': [84307934393430, 3437629559701230, 85621839894847, 4934975208295326], 'label': '768.1090131.32.d1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.d1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.d1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521463
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '32.d1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.d1.d1', '16.b1.b2'], 'contains': ['64.c2.b2', '96.bx1.d2', '128.b1.b1'], 'core': '768.a1.a1', 'coset_action_label': '32T34999', 'count': 16, 'diagramx': [254, -1, 555, -1, 452, -1, 9137, -1], 'generators': [84307934393430, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.32.d1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '32.d1.d2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.d1.d2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521464
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': ['16.b1.b2', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.ba1.b1', '24.bv1.a1', '24.bv1.b1', '24.bw1.b1'], 'contains': ['96.be1.a1', '96.bq1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1980, 2310, 2115, 6373, 2257, 5920, 7708, 4071], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286], 'label': '768.1090131.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521465
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.b1', 'complements': ['16.b1.a2', '16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.a1.b1', '24.ba1.a1', '24.bv1.c1', '24.bv1.d1', '24.bw1.a1'], 'contains': ['96.be1.b1', '96.bq1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1980, 2310, 3815, 4069, 2257, 5920, 5841, 2613], 'generators': [1822337812123926, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.a1.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.a1.b1', 'normal_contained_in': ['12.a1.a1', '24.a1.b1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.b1', 'projective_image': '768.1090131', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521466
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['16.b1.b2', '16.b1.b1', '16.b1.a2', '16.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.bj1.a1', '24.bu1.a1', '24.ca1.a1', '24.ca1.b1'], 'contains': ['96.bt1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8261, 4452, 9235, 2495, 7968, 3998, 1191, 5529], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1179668884439070], 'label': '768.1090131.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.a1.a1', '24.b1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521467
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.a1', '12.m1.c1', '12.n1.a1', '12.n1.c1', '12.t1.a1', '12.v1.a1', '12.x1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6951, -1, 5971, -1, 6162, -1, 3990, -1], 'generators': [4415227175929, 1558496692068486, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.6.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521468
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.i1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.e1.a1', '96.s1.a1', '96.s1.b1', '96.y1.a1', '96.y1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5605, -1, 4091, -1, 5967, -1, 5270, -1], 'generators': [4047630492625, 1822038947023848, 4047630492624, 359890668365808], 'label': '768.1090131.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521469
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.i1.b1'], 'contains': ['96.b1.b1', '96.c1.a1', '96.e1.a1', '96.s1.c1', '96.s1.d1', '96.y1.c1', '96.y1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5605, -1, 5005, -1, 5967, -1, 4849, -1], 'generators': [4047630492625, 4088283555510366, 4047630492624, 359890668365808], 'label': '768.1090131.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.c1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521470
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.i1.a1'], 'contains': ['96.b1.a1', '96.c1.a1', '96.g1.a1', '96.j1.a1', '96.t1.a1', '96.z1.a1', '96.z1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2214, -1, 2342, -1, 4924, -1, 7151, -1], 'generators': [4047630492625, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521471
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.b1', '24.i1.b1'], 'contains': ['96.b1.b1', '96.c1.a1', '96.g1.b1', '96.j1.b1', '96.t1.b1', '96.z1.c1', '96.z1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2214, -1, 3182, -1, 4924, -1, 6628, -1], 'generators': [4047630492625, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.d1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521472
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.a1', '24.i1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '96.u1.a1', '96.ba1.a1', '96.ba1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2978, -1, 3771, -1, 5355, -1, 6262, -1], 'generators': [312321447414, 1821036378652951, 359890668365808, 1821036378652950], 'label': '768.1090131.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521473
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.b1', '24.i1.b1'], 'contains': ['96.b1.b1', '96.e1.a1', '96.u1.b1', '96.ba1.c1', '96.ba1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2978, -1, 5400, -1, 5355, -1, 5351, -1], 'generators': [1821036378652951, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521474
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.l1.a1'], 'contains': ['96.b1.a1', '96.h1.a1', '96.k1.a1', '96.bb1.a1', '96.bb1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1035, -1, 1478, -1, 1363, -1, 8474, -1], 'generators': [4415227175929, 312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521475
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.l1.b1'], 'contains': ['96.b1.b1', '96.h1.b1', '96.k1.b1', '96.bb1.c1', '96.bb1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1035, -1, 2984, -1, 1363, -1, 6814, -1], 'generators': [3844916347312825, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.f1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521476
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.m1.a1'], 'contains': ['96.b1.a1', '96.b1.b1', '96.d1.a1', '96.q1.a1', '96.q1.b1', '96.w1.a1', '96.bc1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6764, -1, 5506, -1, 6771, -1, 3726, -1], 'generators': [1822337812123926, 1, 461960891286, 3846242716609368], 'label': '768.1090131.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521477
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1'], 'contains': ['96.b2.a1', '96.b2.b1', '96.f1.a1', '96.r1.a1', '96.r1.b1', '96.x1.a1', '96.bd1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3220, -1, 6941, -1, 2528, -1, 5657, -1], 'generators': [359890668365808, 1, 735925055088, 3846242716609368], 'label': '768.1090131.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '48.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521478
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.g1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.m1.b1', '12.m1.d1', '12.n1.b1', '12.n1.d1', '12.t1.a1', '12.v1.b1', '12.x1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6951, -1, 6109, -1, 6162, -1, 3460, -1], 'generators': [4047630492625, 1558496692068486, 359890668365808, 1822337812123926, 4415227175928, 312321447414, 1179562541714328], 'label': '768.1090131.6.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.g1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.g1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521479
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.b2.a1', '96.i1.a1', '96.i2.a1', '96.i2.a2', '96.l1.a1', '96.l1.a2', '96.l2.a1', '96.v1.a1', '96.v2.a1', '96.be1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1137, -1, 1268, -1, 1232, -1, 8635, -1], 'generators': [1822337812123926, 312321447414, 1, 461960891286], 'label': '768.1090131.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521480
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.e1.b1', '24.f1.b1'], 'contains': ['96.b1.b1', '96.b2.b1', '96.i1.b1', '96.i2.b1', '96.i2.b2', '96.l1.b1', '96.l1.b2', '96.l2.b1', '96.v1.b1', '96.v2.b1', '96.be1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1137, -1, 3078, -1, 1232, -1, 6880, -1], 'generators': [1822337812123926, 1, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521481
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.o1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.e1.a1', '96.bf1.a1', '96.bf1.b1', '96.bg1.a1', '96.bg1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6889, -1, 7043, -1, 7334, -1, 3067, -1], 'generators': [4047630492625, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521482
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.g1.a1', '24.o1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.bh1.a1', '96.bi1.a1', '96.bi1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7971, -1, 7438, -1, 8501, -1, 1820, -1], 'generators': [4047630492625, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521483
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.h1.a1', '24.o1.a1'], 'contains': ['96.d1.a1', '96.e1.a1', '96.bj1.a1', '96.bl1.a1', '96.bl1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8167, -1, 7990, -1, 8753, -1, 984, -1], 'generators': [1821036378652951, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521484
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '24.p1.a1'], 'contains': ['96.d1.a1', '96.f1.a1', '96.bk1.a1', '96.bm1.a1', '96.bn1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9410, -1, 9410, -1, 9266, -1, 649, -1], 'generators': [1179762397854126, 3846541581724590, 1, 795533260057254], 'label': '768.1090131.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.m1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521485
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '24.q1.a1'], 'contains': ['96.d1.a1', '96.bo1.a1', '96.bo1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9897, -1, 9905, -1, 9525, -1, 136, -1], 'generators': [4088009123503584, 359890668365808, 3845532940242606, 3845532940242607], 'label': '768.1090131.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.n1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521486
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.b2.a1', '96.m1.a1', '96.m2.a1', '96.bp1.a1', '96.bq1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2548, -1, 4031, -1, 3742, -1, 6134, -1], 'generators': [1822337812123926, 359890668365808, 1, 461960891286], 'label': '768.1090131.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521487
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.i1.b1', '24.j1.b1', '24.k1.b1', '24.l1.b1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.a1.a1', '96.b1.b1', '96.b2.b1', '96.m1.b1', '96.m2.b1', '96.bp1.b1', '96.bq1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2548, -1, 5557, -1, 3742, -1, 5059, -1], 'generators': [1822337812123926, 359890668365808, 1, 3846242716609368], 'label': '768.1090131.48.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.o1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521488
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.i1.a1', '24.i1.b1', '24.o1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.e1.a1', '96.n1.a1', '96.n1.b1', '96.br1.a1', '96.br1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3631, -1, 6385, -1, 5817, -1, 4999, -1], 'generators': [1822337812123926, 4047630492625, 4047630492624, 359890668365808], 'label': '768.1090131.48.p1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.p1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521489
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.v1.a1', '12.x1.b1', '12.y1.a1', '12.y1.c1', '12.z1.b1', '12.z1.d1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6461, -1, 5558, -1, 5533, -1, 4294, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.6.h1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521490
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.j1.a1', '24.j1.b1', '24.m1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.o1.a1', '96.bs1.a1', '96.bt1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7845, -1, 8873, -1, 8340, -1, 1307, -1], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1], 'label': '768.1090131.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.q1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521491
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.j1.b1', '24.k1.a1', '24.k1.b1', '24.n1.a1', '24.p1.a1', '24.r1.a1'], 'contains': ['96.a1.a1', '96.f1.a1', '96.p1.a1', '96.bu1.a1', '96.bv1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4275, -1, 8448, -1, 3997, -1, 2334, -1], 'generators': [1822337812123926, 3846884234706384, 359890668365808, 1], 'label': '768.1090131.48.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.r1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521492
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.e1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.i2.a1', '96.bw1.a1', '96.bw1.b1', '96.bx1.a1', '96.bx1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [563, -1, 665, -1, 961, -1, 9345, -1], 'generators': [4047630492625, 4047630492624, 359728823398326, 1821883084207920], 'label': '768.1090131.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.s1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521493
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a2', '24.e1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.i2.a2', '96.bw1.a2', '96.bw1.b2', '96.bx1.a2', '96.bx1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [563, -1, 718, -1, 961, -1, 9420, -1], 'generators': [4047630492625, 312321447414, 4047630492624, 461960891286], 'label': '768.1090131.48.s1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.s1.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521494
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.e1.b1'], 'contains': ['96.g1.b1', '96.h1.b1', '96.i2.b1', '96.bw1.c1', '96.bw1.d1', '96.bx1.c1', '96.bx1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [563, -1, 2025, -1, 961, -1, 7361, -1], 'generators': [4047630492625, 4047630492624, 3437629559701230, 4934975208295326], 'label': '768.1090131.48.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.s1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521495
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b2', '24.e1.b1'], 'contains': ['96.g1.b1', '96.h1.b1', '96.i2.b2', '96.bw1.c2', '96.bw1.d2', '96.bx1.c2', '96.bx1.d2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [563, -1, 2074, -1, 961, -1, 7436, -1], 'generators': [4047630492625, 4047630492624, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.s1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.s1.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521496
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1'], 'contains': ['96.j1.a1', '96.k1.a1', '96.l1.a1', '96.bw1.a1', '96.bw1.b1', '96.bx1.a2', '96.bx1.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [909, -1, 933, -1, 1111, -1, 9194, -1], 'generators': [312321447414, 356012206670569, 4047630492624, 461960891286], 'label': '768.1090131.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.t1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521497
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1'], 'contains': ['96.j1.a1', '96.k1.a1', '96.l1.a2', '96.bw1.a2', '96.bw1.b2', '96.bx1.a1', '96.bx1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [909, -1, 864, -1, 1111, -1, 9270, -1], 'generators': [356012206670569, 4047630492624, 359728823398326, 1821883084207920], 'label': '768.1090131.48.t1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.t1.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521498
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1'], 'contains': ['96.j1.b1', '96.k1.b1', '96.l1.b1', '96.bw1.c2', '96.bw1.d2', '96.bx1.c1', '96.bx1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [909, -1, 2238, -1, 1111, -1, 7211, -1], 'generators': [356012206670569, 4047630492624, 3437629559701230, 4934975208295326], 'label': '768.1090131.48.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.t1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521499
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1'], 'contains': ['96.j1.b1', '96.k1.b1', '96.l1.b2', '96.bw1.c1', '96.bw1.d1', '96.bx1.c2', '96.bx1.d2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [909, -1, 2288, -1, 1111, -1, 7286, -1], 'generators': [356012206670569, 4047630492624, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.t1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.t1.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521500
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '6.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '512.406983', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.v1.b1', '12.x1.a1', '12.y1.b1', '12.y1.d1', '12.z1.a1', '12.z1.c1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6461, -1, 5482, -1, 5533, -1, 4407, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.6.h1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.h1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.h1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521501
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.m1.a1', '96.n1.a1', '96.n1.b1', '96.t1.a1', '96.u1.a1', '96.y1.a1', '96.y1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4901, -1, 4211, -1, 5667, -1, 4924, -1], 'generators': [4047630492625, 1822038947023848, 359890668365808, 1821036378652950], 'label': '768.1090131.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.u1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521502
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.m1.b1', '96.n1.a1', '96.n1.b1', '96.t1.b1', '96.u1.b1', '96.y1.c1', '96.y1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4901, -1, 5146, -1, 5667, -1, 4774, -1], 'generators': [4047630492625, 4088283555510366, 359890668365808, 1821036378652950], 'label': '768.1090131.48.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.u1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521503
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.b1', '24.t1.a1'], 'contains': ['96.m1.a1', '96.n1.a1', '96.s1.a1', '96.z1.a1', '96.ba1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3104, -1, 3643, -1, 5194, -1, 6418, -1], 'generators': [312321447414, 1821036378652951, 4047630492624, 359890668365808], 'label': '768.1090131.48.u2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.u2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u2.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521504
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.a1', '24.t1.b1'], 'contains': ['96.m1.a1', '96.n1.b1', '96.s1.b1', '96.z1.b1', '96.ba1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3104, -1, 3717, -1, 5194, -1, 6568, -1], 'generators': [4047630492625, 312321447414, 359890668365808, 1821036378652950], 'label': '768.1090131.48.u2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.u2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u2.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521505
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.b1', '24.t1.c1'], 'contains': ['96.m1.b1', '96.n1.a1', '96.s1.c1', '96.z1.c1', '96.ba1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3104, -1, 4874, -1, 5194, -1, 5431, -1], 'generators': [1821036378652951, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.u2.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.u2.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u2.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521506
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.u2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.a1', '24.t1.d1'], 'contains': ['96.m1.b1', '96.n1.b1', '96.s1.d1', '96.z1.d1', '96.ba1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3104, -1, 5094, -1, 5194, -1, 5506, -1], 'generators': [4047630492625, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.48.u2.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.u2.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u2.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521507
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.t1.a1', '24.t1.b1'], 'contains': ['96.m1.a1', '96.bb1.a1', '96.bb1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1897, -1, 1978, -1, 2150, -1, 8101, -1], 'generators': [4415227175929, 312321447414, 1820581643595246, 359890668365808], 'label': '768.1090131.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.v1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521508
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '24.t1.c1', '24.t1.d1'], 'contains': ['96.m1.b1', '96.bb1.c1', '96.bb1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1897, -1, 3360, -1, 2150, -1, 6080, -1], 'generators': [3844916347312825, 359890668365808, 1179562541714328, 4930927581391230], 'label': '768.1090131.48.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.v1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521509
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.m1.a1', '96.m1.b1', '96.o1.a1', '96.q1.a1', '96.q1.b1', '96.w1.a1', '96.bc1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7015, -1, 5454, -1, 6621, -1, 3651, -1], 'generators': [1822337812123926, 359890668365809, 461960891286, 3846242716609368], 'label': '768.1090131.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.w1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521510
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1'], 'contains': ['96.m2.a1', '96.m2.b1', '96.p1.a1', '96.r1.a1', '96.r1.b1', '96.x1.a1', '96.bd1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2852, -1, 7181, -1, 2378, -1, 5582, -1], 'generators': [1822337812123927, 359890668365808, 735925055088, 3846242716609368], 'label': '768.1090131.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '48.x1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521511
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.c1.a1', '24.a1.a1', '32.a1.a1', '32.b1.a1', '32.b2.a1', '32.b2.a2'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [573, -1, 376, -1, 597, -1, 9622, -1], 'generators': [84307934393430, 1822337812123926, 84307934393431, 312321447414, 359890668365808, 461960891286], 'label': '768.1090131.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521512
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.t1.a1', '24.t1.b1'], 'contains': ['96.l1.a1', '96.l1.a2', '96.l2.a1', '96.m1.a1', '96.m2.a1', '96.v1.a1', '96.v2.a1', '96.be1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1590, -1, 1606, -1, 1495, -1, 8258, -1], 'generators': [1822337812123926, 312321447414, 359890668365809, 461960891286], 'label': '768.1090131.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.y1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521513
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.t1.c1', '24.t1.d1'], 'contains': ['96.l1.b1', '96.l1.b2', '96.l2.b1', '96.m1.b1', '96.m2.b1', '96.v1.b1', '96.v2.b1', '96.be1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1590, -1, 3437, -1, 1495, -1, 6673, -1], 'generators': [1822337812123926, 359890668365809, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.y1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521514
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.s1.a1', '24.s1.b1'], 'contains': ['96.n1.a1', '96.n1.b1', '96.o1.a1', '96.bg1.a1', '96.bg1.b1', '96.bh1.a1', '96.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7591, -1, 6998, -1, 7572, -1, 2998, -1], 'generators': [4047630492625, 359890668365808, 1821036378652950, 1179668884439070], 'label': '768.1090131.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.z1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521515
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.z2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.s1.b1', '24.u1.a1'], 'contains': ['96.n1.a1', '96.o1.a1', '96.bf1.a1', '96.bi1.a1', '96.bl1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8069, -1, 7856, -1, 8627, -1, 1238, -1], 'generators': [1821036378652951, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.48.z2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.z2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z2.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521516
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.z2', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.s1.a1', '24.u1.b1'], 'contains': ['96.n1.b1', '96.o1.a1', '96.bf1.b1', '96.bi1.b1', '96.bl1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8069, -1, 7948, -1, 8627, -1, 1375, -1], 'generators': [4047630492625, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.48.z2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.z2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z2.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521517
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.u1.a1', '24.u1.b1'], 'contains': ['96.o1.a1', '96.p1.a1', '96.bk1.a1', '96.bm1.a1', '96.bn1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8955, -1, 9460, -1, 9005, -1, 574, -1], 'generators': [1179762397854126, 3846541581724590, 1822337812123927, 795533260057254], 'label': '768.1090131.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.ba1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521518
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.u1.a1', '24.u1.b1'], 'contains': ['96.o1.a1', '96.bo1.a1', '96.bo1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9308, -1, 9844, -1, 9396, -1, 72, -1], 'generators': [4930298537645568, 4088009123503584, 359890668365808, 3845532940242607], 'label': '768.1090131.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bb1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521519
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.b1', '24.v1.a1'], 'contains': ['96.q1.a1', '96.s1.a1', '96.u1.a1', '96.y1.c1', '96.ba1.d1', '96.bf1.a1', '96.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6102, -1, 5755, -1, 6243, -1, 3537, -1], 'generators': [4088283555510366, 4047630492624, 359890668365808, 1820781140537905], 'label': '768.1090131.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bc1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521520
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.a1', '24.v1.a1'], 'contains': ['96.q1.a1', '96.s1.b1', '96.u1.a1', '96.y1.d1', '96.ba1.c1', '96.bf1.b1', '96.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6102, -1, 6132, -1, 6243, -1, 3587, -1], 'generators': [4253081604151, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.48.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bc1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521521
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.b1', '24.v1.b1'], 'contains': ['96.q1.b1', '96.s1.c1', '96.u1.b1', '96.y1.a1', '96.ba1.b1', '96.bf1.a1', '96.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6102, -1, 5648, -1, 6243, -1, 3789, -1], 'generators': [4084267591005871, 1822038947023848, 4047630492624, 359890668365808], 'label': '768.1090131.48.bc1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bc1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521522
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.b1'], 'contains': ['16.c1.b1', '24.a1.b1', '32.a1.a1', '32.b1.b1', '32.b2.b1', '32.b2.b2'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [573, -1, 985, -1, 597, -1, 8101, -1], 'generators': [84307934393430, 1822337812123926, 84307934393431, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.8.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.a1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521523
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.a1', '24.v1.b1'], 'contains': ['96.q1.b1', '96.s1.d1', '96.u1.b1', '96.y1.b1', '96.ba1.a1', '96.bf1.b1', '96.bj1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6102, -1, 5788, -1, 6243, -1, 3839, -1], 'generators': [312321447414, 1183459680839575, 359890668365808, 1821036378652950], 'label': '768.1090131.48.bc1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bc1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521524
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.a1', '24.v1.a1'], 'contains': ['96.q1.a1', '96.s1.b1', '96.t1.a1', '96.y1.c1', '96.z1.d1', '96.bf1.b1', '96.bh1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6418, -1, 4774, -1, 6117, -1, 4127, -1], 'generators': [4253081604151, 4088283555510366, 4047630492624, 359890668365808], 'label': '768.1090131.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bd1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521525
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.b1', '24.v1.a1'], 'contains': ['96.q1.a1', '96.s1.a1', '96.t1.a1', '96.y1.d1', '96.z1.c1', '96.bf1.a1', '96.bh1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6418, -1, 4530, -1, 6117, -1, 4052, -1], 'generators': [4253081604151, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bd1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521526
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.a1', '24.v1.b1'], 'contains': ['96.q1.b1', '96.s1.d1', '96.t1.b1', '96.y1.a1', '96.z1.b1', '96.bf1.b1', '96.bh1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6418, -1, 4924, -1, 6117, -1, 4549, -1], 'generators': [1822038947023848, 1183459680839575, 4047630492624, 359890668365808], 'label': '768.1090131.48.bd1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bd1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521527
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.b1', '24.v1.b1'], 'contains': ['96.q1.b1', '96.s1.c1', '96.t1.b1', '96.y1.b1', '96.z1.a1', '96.bf1.a1', '96.bh1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6418, -1, 4824, -1, 6117, -1, 4474, -1], 'generators': [312321447414, 1183459680839575, 4047630492624, 359890668365808], 'label': '768.1090131.48.bd1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bd1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 68521528
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.t1.a1', '24.bb1.a1'], 'contains': ['96.v1.a1', '96.z1.a1', '96.bb1.a1', '96.bw1.a1', '96.bw1.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1496, -1, 1363, -1, 1765, -1, 8393, -1], 'generators': [4415227175929, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.be1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521529
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.t1.b1', '24.bb1.b1'], 'contains': ['96.v1.a1', '96.z1.b1', '96.bb1.b1', '96.bw1.b1', '96.bw1.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1496, -1, 1547, -1, 1765, -1, 8318, -1], 'generators': [4047630492625, 312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.48.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.be1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521530
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.t1.c1', '24.bb1.c1'], 'contains': ['96.v1.b1', '96.z1.c1', '96.bb1.c1', '96.bw1.c1', '96.bw1.c2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1496, -1, 2931, -1, 1765, -1, 6734, -1], 'generators': [3844916347312825, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.be1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.be1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521531
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.t1.d1', '24.bb1.d1'], 'contains': ['96.v1.b1', '96.z1.d1', '96.bb1.d1', '96.bw1.d1', '96.bw1.d2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1496, -1, 3038, -1, 1765, -1, 6940, -1], 'generators': [4047630492625, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.48.be1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.be1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521532
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.t1.b1', '24.bb1.a1'], 'contains': ['96.v1.a1', '96.ba1.a1', '96.bb1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1697, -1, 1896, -1, 2026, -1, 7977, -1], 'generators': [4415227175929, 312321447414, 359890668365808, 1821036378652950], 'label': '768.1090131.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bf1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521533
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.c1.a1'], 'contains': ['16.d1.a1', '24.b1.a1', '32.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1525, -1, 6283, -1, 1381, -1, 3196, -1], 'generators': [84307934393430, 1822337812123926, 84307934393431, 3846697444535406, 359890668365808, 1179668884439070], 'label': '768.1090131.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68521534
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.t1.a1', '24.bb1.b1'], 'contains': ['96.v1.a1', '96.ba1.b1', '96.bb1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1697, -1, 1855, -1, 2026, -1, 7915, -1], 'generators': [312321447414, 1820581643595246, 1821036378652951, 359890668365808], 'label': '768.1090131.48.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bf1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521535
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.t1.d1', '24.bb1.c1'], 'contains': ['96.v1.b1', '96.ba1.c1', '96.bb1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1697, -1, 3586, -1, 2026, -1, 5957, -1], 'generators': [3844916347312825, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.48.bf1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bf1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521536
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.t1.c1', '24.bb1.d1'], 'contains': ['96.v1.b1', '96.ba1.d1', '96.bb1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1697, -1, 3484, -1, 2026, -1, 5895, -1], 'generators': [1821036378652951, 359890668365808, 1179562541714328, 4930927581391230], 'label': '768.1090131.48.bf1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bf1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
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id: 68521537
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.b1', '24.be1.a1'], 'contains': ['96.s1.a1', '96.s1.c1', '96.u1.a1', '96.u1.b1', '96.w1.a1', '96.bg1.a1', '96.bl1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7476, -1, 6428, -1, 7471, -1, 2948, -1], 'generators': [797114890868809, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bg1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521538
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.a1', '24.be1.a1'], 'contains': ['96.s1.b1', '96.s1.d1', '96.u1.a1', '96.u1.b1', '96.w1.a1', '96.bg1.b1', '96.bl1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7476, -1, 6746, -1, 7471, -1, 3135, -1], 'generators': [797114890868809, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.48.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bg1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521539
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.a1', '24.be1.a1'], 'contains': ['96.s1.b1', '96.s1.d1', '96.t1.a1', '96.t1.b1', '96.w1.a1', '96.bg1.a1', '96.bi1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7359, -1, 6045, -1, 7173, -1, 3474, -1], 'generators': [4047630492624, 359890668365808, 355744021224607, 1179668884439070], 'label': '768.1090131.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bh1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521540
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.b1', '24.be1.a1'], 'contains': ['96.s1.a1', '96.s1.c1', '96.t1.a1', '96.t1.b1', '96.w1.a1', '96.bg1.b1', '96.bi1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7359, -1, 5603, -1, 7173, -1, 3399, -1], 'generators': [797114890868809, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.48.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bh1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521541
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.a1', '24.bo1.a1'], 'contains': ['96.y1.a1', '96.y1.c1', '96.ba1.a1', '96.ba1.c1', '96.bc1.a1', '96.bg1.a1', '96.bl1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7115, -1, 5242, -1, 7047, -1, 4410, -1], 'generators': [312321447414, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bi1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521542
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.s1.b1', '24.bo1.b1'], 'contains': ['96.y1.b1', '96.y1.d1', '96.ba1.b1', '96.ba1.d1', '96.bc1.a1', '96.bg1.b1', '96.bl1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7115, -1, 5046, -1, 7047, -1, 4360, -1], 'generators': [1779365211990169, 1558054095215088, 735925055088, 795533260057254], 'label': '768.1090131.48.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bi1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521543
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.b1', '24.bo1.a1'], 'contains': ['96.y1.a1', '96.y1.c1', '96.z1.a1', '96.z1.c1', '96.bc1.a1', '96.bg1.a1', '96.bi1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7225, -1, 4161, -1, 6921, -1, 4624, -1], 'generators': [312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bj1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521544
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['16.e1.a1', '24.r1.a1', '32.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1235, -1, 5415, -1, 1092, -1, 6212, -1], 'generators': [84307934393430, 84307934393431, 1558496692068486, 359890668365808, 3846541581724590, 1822337812123926], 'label': '768.1090131.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
-
id: 68521545
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.s1.a1', '24.bo1.b1'], 'contains': ['96.y1.b1', '96.y1.d1', '96.z1.b1', '96.z1.d1', '96.bc1.a1', '96.bg1.b1', '96.bi1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7225, -1, 4260, -1, 6921, -1, 4699, -1], 'generators': [1558054095215088, 735925055088, 795533260057254, 85621839894847], 'label': '768.1090131.48.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bj1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521546
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.t1.a1', '24.bv1.a1'], 'contains': ['96.z1.a1', '96.bb1.b1', '96.be1.a1', '96.bx1.a1', '96.bx1.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1230, -1, 1229, -1, 1615, -1, 8695, -1], 'generators': [312321447414, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bk1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521547
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.t1.b1', '24.bv1.b1'], 'contains': ['96.z1.b1', '96.bb1.a1', '96.be1.a1', '96.bx1.b1', '96.bx1.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1230, -1, 1176, -1, 1615, -1, 8770, -1], 'generators': [312321447414, 461960891286, 795533260057254, 85621839894847], 'label': '768.1090131.48.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bk1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521548
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.t1.c1', '24.bv1.c1'], 'contains': ['96.z1.c1', '96.bb1.d1', '96.be1.b1', '96.bx1.c1', '96.bx1.c2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1230, -1, 2880, -1, 1615, -1, 7015, -1], 'generators': [4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.bk1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bk1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521549
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.t1.d1', '24.bv1.d1'], 'contains': ['96.z1.d1', '96.bb1.c1', '96.be1.b1', '96.bx1.d1', '96.bx1.d2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1230, -1, 2827, -1, 1615, -1, 7090, -1], 'generators': [1558054095215088, 3846242716609368, 795533260057254, 85621839894847], 'label': '768.1090131.48.bk1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bk1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521550
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.t1.b1', '24.bv1.a1'], 'contains': ['96.ba1.a1', '96.bb1.b1', '96.be1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 1937, -1, 1902, -1, 8039, -1], 'generators': [312321447414, 359890668365808, 461960891286, 1821036378652950], 'label': '768.1090131.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bl1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521551
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1', '24.t1.a1', '24.bv1.b1'], 'contains': ['96.ba1.b1', '96.bb1.a1', '96.be1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 1814, -1, 1902, -1, 8162, -1], 'generators': [312321447414, 1779365211990169, 461960891286, 795533260057254], 'label': '768.1090131.48.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.bl1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521552
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.t1.d1', '24.bv1.c1'], 'contains': ['96.ba1.c1', '96.bb1.d1', '96.be1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 3401, -1, 1902, -1, 6188, -1], 'generators': [359890668365808, 1821036378652950, 1558054095215088, 3846242716609368], 'label': '768.1090131.48.bl1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bl1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.c1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521553
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1', '24.t1.c1', '24.bv1.d1'], 'contains': ['96.ba1.d1', '96.bb1.c1', '96.be1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1338, -1, 3269, -1, 1902, -1, 6019, -1], 'generators': [1779365211990169, 1558054095215088, 3846242716609368, 795533260057254], 'label': '768.1090131.48.bl1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.bl1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.d1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521554
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.u1.a1', '24.by1.a1'], 'contains': ['96.bi1.a1', '96.bm1.a1', '96.bo1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9591, -1, 9541, -1, 9653, -1, 455, -1], 'generators': [1558496692068486, 4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bm1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521555
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.b1.a1'], 'contains': ['16.c1.a1', '24.bv1.a1', '32.c1.a1', '32.d1.a1', '32.d1.a2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [752, -1, 322, -1, 844, -1, 9043, -1], 'generators': [84307934393430, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.8.d1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.d1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521557
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.u1.a1', '24.bz1.a1'], 'contains': ['96.bi1.a1', '96.bn1.a1', '96.bo1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9678, -1, 9621, -1, 9760, -1, 299, -1], 'generators': [4047630492624, 4088009123503584, 359890668365808, 3845532940242607], 'label': '768.1090131.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bn1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521558
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.u1.b1', '24.bz1.b1'], 'contains': ['96.bi1.b1', '96.bn1.a1', '96.bo1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9678, -1, 9658, -1, 9760, -1, 402, -1], 'generators': [4047630492625, 4088009123503584, 359890668365808, 3845532940242606], 'label': '768.1090131.48.bn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bn1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521559
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.u1.b1', '24.by1.a1'], 'contains': ['96.bl1.a1', '96.bm1.a1', '96.bo1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9507, -1, 9727, -1, 9864, -1, 350, -1], 'generators': [1558496692068486, 4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bo1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521560
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.u1.a1', '24.by1.b1'], 'contains': ['96.bl1.b1', '96.bm1.a1', '96.bo1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9507, -1, 9693, -1, 9864, -1, 247, -1], 'generators': [1179762397854126, 3846541581724590, 1779365211990169, 795533260057254], 'label': '768.1090131.48.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bo1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521561
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.u1.b1', '24.bz1.a1'], 'contains': ['96.bl1.a1', '96.bn1.a1', '96.bo1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9765, -1, 9791, -1, 9961, -1, 19, -1], 'generators': [4088009123503584, 359890668365808, 1821036378652950, 3845532940242607], 'label': '768.1090131.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bp1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521562
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.h1.a1', '24.u1.a1', '24.bz1.b1'], 'contains': ['96.bl1.b1', '96.bn1.a1', '96.bo1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9765, -1, 9759, -1, 9961, -1, 198, -1], 'generators': [4930298537645568, 1821036378652951, 4088009123503584, 359890668365808], 'label': '768.1090131.48.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.bp1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521563
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.v1.a1', '24.x1.a1', '24.y1.a1', '24.ba1.a1', '24.bc1.a1', '24.bk1.a1'], 'contains': ['96.q1.a1', '96.bp1.a1', '96.bq1.b1', '96.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 6566, -1, 4679, -1, 2810, -1], 'generators': [1822337812123926, 461960891287, 359890668365808, 3846242716609368], 'label': '768.1090131.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bq1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521564
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.v1.b1', '24.x1.b1', '24.y1.b1', '24.ba1.b1', '24.bc1.b1', '24.bk1.b1'], 'contains': ['96.q1.b1', '96.bp1.b1', '96.bq1.a1', '96.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3936, -1, 7097, -1, 4679, -1, 2885, -1], 'generators': [1822337812123926, 3846242716609369, 359890668365808, 461960891286], 'label': '768.1090131.48.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bq1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521565
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.w1.a1', '24.z1.a1', '24.ba1.a1', '24.bc1.a1', '24.bd1.a1', '24.bl1.a1'], 'contains': ['96.r1.a1', '96.bp1.a1', '96.bq1.b1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4402, -1, 6892, -1, 3621, -1, 2535, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 3846242716609368], 'label': '768.1090131.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.br1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521566
{'ambient': '768.1090131', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['384.a1.a1', '384.b1.a1', '384.d1.a1', '384.d1.b1', '384.f1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.h1.a1', '8.d1.a1', '8.d1.c1', '8.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1464, 2258, 986, 3052, 1397, 2802, 6278, 836], 'generators': [84307934393430, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68521567
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '4.b1.a1'], 'contains': ['16.c1.a1', '24.bv1.b1', '32.c1.b1', '32.d1.b1', '32.d1.b2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [752, -1, 445, -1, 844, -1, 9146, -1], 'generators': [84307934393430, 1822337812123926, 312321447414, 359890668365808, 461960891286, 85621839894847], 'label': '768.1090131.8.d1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.d1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521568
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.w1.b1', '24.z1.b1', '24.ba1.b1', '24.bc1.b1', '24.bd1.b1', '24.bl1.b1'], 'contains': ['96.r1.b1', '96.bp1.b1', '96.bq1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4402, -1, 7313, -1, 3621, -1, 2611, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 1558054095215089], 'label': '768.1090131.48.br1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.br1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521569
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.v1.a1', '24.be1.a1'], 'contains': ['96.s1.a1', '96.s1.b1', '96.t1.a1', '96.u1.a1', '96.bp1.a1', '96.br1.a1', '96.br1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3819, -1, 5712, -1, 5516, -1, 3977, -1], 'generators': [1822337812123926, 4253081604151, 4047630492624, 359890668365808], 'label': '768.1090131.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bs1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521570
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.v1.b1', '24.be1.a1'], 'contains': ['96.s1.c1', '96.s1.d1', '96.t1.b1', '96.u1.b1', '96.bp1.b1', '96.br1.a1', '96.br1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3819, -1, 6336, -1, 5516, -1, 3902, -1], 'generators': [1822337812123926, 1183459680839575, 4047630492624, 359890668365808], 'label': '768.1090131.48.bs1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.bs1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521571
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.w1.a1', '24.y1.a1', '24.bc1.a1', '24.bf1.a1', '24.bg1.a1', '24.bk1.b1'], 'contains': ['96.bp1.a1', '96.bs1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5007, -1, 8077, -1, 4145, -1, 1950, -1], 'generators': [1822337812123926, 3846697444535407, 3846884234706384, 359890668365808], 'label': '768.1090131.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bt1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521572
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.w1.b1', '24.y1.b1', '24.bc1.b1', '24.bf1.a1', '24.bg1.a1', '24.bk1.a1'], 'contains': ['96.bp1.b1', '96.bs1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5007, -1, 8036, -1, 4145, -1, 1631, -1], 'generators': [1822337812123926, 1179562541714329, 3846884234706384, 359890668365808], 'label': '768.1090131.48.bt1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bt1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521573
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.y1.a1', '24.z1.a1', '24.bd1.a1', '24.bh1.a1', '24.bj1.a1', '24.bl1.b1'], 'contains': ['96.bp1.a1', '96.bt1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6293, -1, 8800, -1, 4816, -1, 1569, -1], 'generators': [1822337812123926, 312321447415, 3846697444535406, 359890668365808], 'label': '768.1090131.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bu1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521574
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.y1.b1', '24.z1.b1', '24.bd1.b1', '24.bh1.a1', '24.bj1.a1', '24.bl1.a1'], 'contains': ['96.bp1.b1', '96.bt1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6293, -1, 8679, -1, 4816, -1, 1507, -1], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1558054095215089], 'label': '768.1090131.48.bu1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bu1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521575
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.w1.a1', '24.z1.a1', '24.bc1.a1', '24.bf1.a1', '24.bh1.a1', '24.bl1.b1'], 'contains': ['96.bp1.a1', '96.bu1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4725, -1, 8160, -1, 3360, -1, 2260, -1], 'generators': [1822337812123926, 461960891287, 3846884234706384, 359890668365808], 'label': '768.1090131.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bv1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521576
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.w1.b1', '24.z1.b1', '24.bc1.b1', '24.bf1.a1', '24.bh1.a1', '24.bl1.a1'], 'contains': ['96.bp1.b1', '96.bu1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4725, -1, 8118, -1, 3360, -1, 2198, -1], 'generators': [1822337812123926, 3846884234706384, 359890668365808, 1558054095215089], 'label': '768.1090131.48.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bv1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521577
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.bb1.a1', '24.bb1.b1', '24.bc1.a1', '24.bd1.a1', '24.bk1.b1', '24.bl1.b1'], 'contains': ['96.v1.a1', '96.v2.a1', '96.bp1.a1', '96.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2477, -1, 2480, -1, 2738, -1, 7517, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 461960891286], 'label': '768.1090131.48.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bw1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521578
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.b1.b1'], 'contains': ['16.c1.b1', '24.bv1.c1', '32.c1.a1', '32.d1.c1', '32.d1.c2'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [752, -1, 930, -1, 844, -1, 8204, -1], 'generators': [84307934393430, 1822337812123926, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.8.d1.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.d1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.c1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521579
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '48.bw1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.bb1.c1', '24.bb1.d1', '24.bc1.b1', '24.bd1.b1', '24.bk1.a1', '24.bl1.a1'], 'contains': ['96.v1.b1', '96.v2.b1', '96.bp1.b1', '96.bq1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2477, -1, 4965, -1, 2738, -1, 4188, -1], 'generators': [1822337812123926, 359890668365808, 3846242716609368, 1558054095215089], 'label': '768.1090131.48.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bw1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521580
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.bx1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.be1.a1', '24.bg1.a1', '24.bi1.a1', '24.bj1.a1', '24.bl1.a1', '24.bl1.b1'], 'contains': ['96.w1.a1', '96.bp1.a1', '96.bp1.b1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8543, -1, 7790, -1, 7848, -1, 1745, -1], 'generators': [1822337812123926, 3846697444535406, 3846242716609369, 359890668365808], 'label': '768.1090131.48.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bx1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521581
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.by1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.bf1.a1', '24.bh1.a1', '24.bk1.a1', '24.bk1.b1', '24.bl1.a1', '24.bl1.b1'], 'contains': ['96.x1.a1', '96.bp1.a1', '96.bp1.b1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4578, -1, 7388, -1, 3009, -1, 2460, -1], 'generators': [1822337812123926, 3846242716609369, 3846884234706384, 359890668365808], 'label': '768.1090131.48.by1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.by1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.by1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521582
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.v1.b1', '24.bb1.a1', '24.bm1.a1', '24.bn1.a1', '24.bo1.a1', '24.bv1.a1'], 'contains': ['96.y1.a1', '96.z1.a1', '96.ba1.a1', '96.bq1.a1', '96.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2383, -1, 3222, -1, 5044, -1, 6342, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.48.bz1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.bz1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521583
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.v1.b1', '24.bb1.b1', '24.bm1.b1', '24.bn1.b1', '24.bo1.b1', '24.bv1.b1'], 'contains': ['96.y1.b1', '96.z1.b1', '96.ba1.b1', '96.bq1.a1', '96.br1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2383, -1, 3314, -1, 5044, -1, 6493, -1], 'generators': [1822337812123926, 359890668365808, 735925055088, 85621839894847], 'label': '768.1090131.48.bz1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.bz1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521584
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.v1.a1', '24.bb1.c1', '24.bm1.c1', '24.bn1.c1', '24.bo1.a1', '24.bv1.c1'], 'contains': ['96.y1.c1', '96.z1.c1', '96.ba1.c1', '96.bq1.b1', '96.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2383, -1, 4621, -1, 5044, -1, 5120, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.48.bz1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bz1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521585
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.bz1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.v1.a1', '24.bb1.d1', '24.bm1.d1', '24.bn1.d1', '24.bo1.b1', '24.bv1.d1'], 'contains': ['96.y1.d1', '96.z1.d1', '96.ba1.d1', '96.bq1.b1', '96.br1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2383, -1, 4426, -1, 5044, -1, 5195, -1], 'generators': [1822337812123926, 359890668365808, 1558054095215088, 85621839894847], 'label': '768.1090131.48.bz1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.bz1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bz1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521586
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.w1.b1', '24.y1.b1', '24.ba1.b1', '24.bc1.a1', '24.bp1.a1', '24.bq1.a1'], 'contains': ['96.bq1.a1', '96.bs1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5381, -1, 7484, -1, 4269, -1, 2136, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 1558428122581231], 'label': '768.1090131.48.ca1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.ca1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521587
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ca1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.w1.a1', '24.y1.a1', '24.ba1.a1', '24.bc1.b1', '24.bp1.a1', '24.bq1.a1'], 'contains': ['96.bq1.b1', '96.bs1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5381, -1, 7574, -1, 4269, -1, 2012, -1], 'generators': [1822337812123926, 359890668365808, 1558428122581231, 3846242716609368], 'label': '768.1090131.48.ca1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.ca1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ca1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521588
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.y1.b1', '24.z1.b1', '24.bl1.b1', '24.br1.a1', '24.bu1.a1', '24.bw1.b1'], 'contains': ['96.bq1.a1', '96.bt1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5104, -1, 8233, -1, 4543, -1, 2074, -1], 'generators': [1822337812123926, 312321447414, 3846697444535406, 359890668365808], 'label': '768.1090131.48.cb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.cb1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521589
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '8.d1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '4.b1.b1'], 'contains': ['16.c1.b1', '24.bv1.d1', '32.c1.b1', '32.d1.d1', '32.d1.d2'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [752, -1, 720, -1, 844, -1, 8286, -1], 'generators': [84307934393430, 1822337812123926, 359890668365808, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.8.d1.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.d1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.d1.d1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521590
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cb1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.y1.a1', '24.z1.a1', '24.bl1.a1', '24.br1.a1', '24.bu1.a1', '24.bw1.a1'], 'contains': ['96.bq1.b1', '96.bt1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5104, -1, 8396, -1, 4543, -1, 1888, -1], 'generators': [1822337812123926, 359890668365808, 1558328613944424, 3846242716609368], 'label': '768.1090131.48.cb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.cb1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cb1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521591
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.w1.b1', '24.bk1.b1', '24.bm1.a1', '24.bm1.b1', '24.br1.a1', '24.bw1.b1'], 'contains': ['96.bq1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 6479, -1, 3237, -1, 4303, -1], 'generators': [1822337812123926, 1179762397854126, 312321447414, 359890668365808], 'label': '768.1090131.48.cc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cc1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521592
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.w1.a1', '24.bk1.a1', '24.bm1.c1', '24.bm1.d1', '24.br1.a1', '24.bw1.a1'], 'contains': ['96.bq1.b1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3327, -1, 7227, -1, 3237, -1, 2741, -1], 'generators': [1558496692068486, 1822337812123926, 359890668365808, 3846242716609368], 'label': '768.1090131.48.cc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cc1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cc1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521593
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.a1', '24.z1.b1', '24.ba1.b1', '24.bd1.a1', '24.bn1.a1', '24.bn1.b1', '24.bp1.a1'], 'contains': ['96.bq1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4160, -1, 6520, -1, 3849, -1, 4242, -1], 'generators': [1822337812123926, 3846541581724591, 359890668365808, 461960891286], 'label': '768.1090131.48.cd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cd1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521594
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.k1.b1', '24.z1.a1', '24.ba1.a1', '24.bd1.b1', '24.bn1.c1', '24.bn1.d1', '24.bp1.a1'], 'contains': ['96.bq1.b1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4160, -1, 7268, -1, 3849, -1, 2679, -1], 'generators': [1822337812123926, 359890668365808, 1558496692068487, 3846242716609368], 'label': '768.1090131.48.cd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cd1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cd1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521595
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.x1.b1', '24.bb1.a1', '24.bm1.b1', '24.bn1.a1', '24.bs1.a1', '24.bv1.b1'], 'contains': ['96.bb1.a1', '96.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2073, -1, 2151, -1, 3484, -1, 7654, -1], 'generators': [1822337812123926, 85895741411455, 359890668365808, 735925055088], 'label': '768.1090131.48.ce1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.ce1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521596
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.x1.b1', '24.bb1.b1', '24.bm1.a1', '24.bn1.b1', '24.bs1.b1', '24.bv1.a1'], 'contains': ['96.bb1.b1', '96.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2073, -1, 2192, -1, 3484, -1, 7592, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.48.ce1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.ce1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521597
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '24.x1.a1', '24.bb1.c1', '24.bm1.d1', '24.bn1.c1', '24.bs1.c1', '24.bv1.d1'], 'contains': ['96.bb1.c1', '96.bq1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2073, -1, 3954, -1, 3484, -1, 5787, -1], 'generators': [1822337812123926, 3824964916138807, 359890668365808, 1558054095215088], 'label': '768.1090131.48.ce1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.ce1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.c1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521598
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '48.ce1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '24.x1.a1', '24.bb1.d1', '24.bm1.c1', '24.bn1.d1', '24.bs1.d1', '24.bv1.c1'], 'contains': ['96.bb1.d1', '96.bq1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2073, -1, 3995, -1, 3484, -1, 5725, -1], 'generators': [1822337812123926, 359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.48.ce1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.ce1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ce1.d1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521599
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cf1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.bd1.a1', '24.bd1.b1', '24.bo1.a1', '24.bo1.b1', '24.bq1.a1', '24.bs1.a1', '24.bs1.b1', '24.bs1.c1', '24.bs1.d1', '24.bt1.a1', '24.bt1.b1', '24.bu1.a1', '24.bw1.a1', '24.bw1.b1'], 'contains': ['96.bc1.a1', '96.bq1.a1', '96.bq1.b1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7690, -1, 5830, -1, 6369, -1, 3324, -1], 'generators': [1822337812123926, 359890668365808, 461960891286, 3846242716609368], 'label': '768.1090131.48.cf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cf1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521600
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '4.c1.a1'], 'contains': ['16.d1.a1', '24.ca1.a1', '32.c1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1700, -1, 6223, -1, 1563, -1, 3287, -1], 'generators': [84307934393430, 1822337812123926, 3846697444535406, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.8.e1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.e1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68521601
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.bc1.a1', '24.bc1.b1', '24.bp1.a1', '24.br1.a1', '24.bw1.a1', '24.bw1.b1'], 'contains': ['96.bd1.a1', '96.bq1.a1', '96.bq1.b1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4054, -1, 6789, -1, 2859, -1, 3249, -1], 'generators': [1822337812123926, 359890668365808, 735925055088, 3846242716609368], 'label': '768.1090131.48.cg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.cg1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cg1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521602
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ch1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.v1.a1', '24.v1.b1'], 'contains': ['96.bf1.a1', '96.bf1.b1', '96.bh1.a1', '96.bj1.a1', '96.br1.a1', '96.br1.b1', '96.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6205, -1, 7139, -1, 6495, -1, 3186, -1], 'generators': [1183572256704511, 1822337812123926, 4047630492624, 359890668365808], 'label': '768.1090131.48.ch1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '48.ch1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ch1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521620
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b2.b1', '32.d1.c1', '32.d1.d1'], 'contains': ['192.t2.b1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [132, -1, 408, -1, 452, -1, 8389, -1], 'generators': [84307934393430, 3437629559701230, 4934975208295326], 'label': '768.1090131.64.c2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '64.c2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521603
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.be1.a1', '24.bo1.a1', '24.bx1.a1', '24.by1.a1', '24.bz1.a1', '24.ca1.a1'], 'contains': ['96.bg1.a1', '96.bi1.a1', '96.bl1.a1', '96.br1.a1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8799, -1, 8529, -1, 8878, -1, 1047, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.48.ci1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.ci1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521604
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.ci1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.be1.a1', '24.bo1.b1', '24.bx1.b1', '24.by1.b1', '24.bz1.b1', '24.ca1.b1'], 'contains': ['96.bg1.b1', '96.bi1.b1', '96.bl1.b1', '96.br1.b1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8799, -1, 7915, -1, 8878, -1, 1098, -1], 'generators': [1822337812123926, 359890668365808, 1558328613944424, 85621839894847], 'label': '768.1090131.48.ci1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.ci1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ci1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521605
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cj1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.w1.a1', '24.w1.b1', '24.y1.a1', '24.y1.b1', '24.bf1.a1', '24.bp1.a1'], 'contains': ['96.bk1.a1', '96.bs1.a1', '96.bu1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5969, -1, 8571, -1, 4406, -1, 1438, -1], 'generators': [1822337812123926, 3846884234706384, 359890668365808, 1558496692068487], 'label': '768.1090131.48.cj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.cj1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521606
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '48.ck1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.y1.a1', '24.y1.b1', '24.bg1.a1', '24.bq1.a1', '24.bx1.a1', '24.bx1.b1'], 'contains': ['96.bs1.a1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8449, -1, 8930, -1, 8058, -1, 1146, -1], 'generators': [1822337812123926, 1179668884439071, 3846697444535406, 359890668365808], 'label': '768.1090131.48.ck1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.ck1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ck1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521607
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cl1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.bg1.a1', '24.bh1.a1', '24.br1.a1', '24.bu1.a1', '24.by1.a1', '24.by1.b1'], 'contains': ['96.bm1.a1', '96.bt1.a1', '96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8355, -1, 9141, -1, 7698, -1, 909, -1], 'generators': [1822337812123926, 1179762397854126, 3846541581724590, 359890668365808], 'label': '768.1090131.48.cl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cl1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cl1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521608
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.p1.a1', '24.z1.a1', '24.z1.b1', '24.bj1.a1', '24.bq1.a1', '24.bz1.a1', '24.bz1.b1'], 'contains': ['96.bn1.a1', '96.bt1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8678, -1, 9193, -1, 8179, -1, 834, -1], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1558428122581231], 'label': '768.1090131.48.cm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.cm1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521609
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bi1.a1', '24.bt1.a1', '24.bx1.a1', '24.by1.b1', '24.bz1.a1', '24.ca1.b1'], 'contains': ['96.bo1.a1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9215, -1, 9330, -1, 9135, -1, 714, -1], 'generators': [1822337812123926, 359890668365808, 3825182759822761, 1558328613944424], 'label': '768.1090131.48.cn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.cn1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521610
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.bi1.a1', '24.bt1.b1', '24.bx1.b1', '24.by1.a1', '24.bz1.b1', '24.ca1.a1'], 'contains': ['96.bo1.b1', '96.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9215, -1, 9366, -1, 9135, -1, 769, -1], 'generators': [1822337812123926, 359890668365808, 3845532940242606, 1179668884439070], 'label': '768.1090131.48.cn1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.cn1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cn1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
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id: 68521611
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '4.c1.a1'], 'contains': ['16.d1.a1', '24.ca1.b1', '32.c1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1700, -1, 6170, -1, 1563, -1, 3365, -1], 'generators': [84307934393430, 1822337812123926, 3846697444535406, 359890668365808, 1179668884439070, 85621839894847], 'label': '768.1090131.8.e1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.e1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1.b1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
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id: 68521612
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.co1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '24.w1.a1', '24.w1.b1', '24.z1.a1', '24.z1.b1', '24.bh1.a1', '24.bp1.a1'], 'contains': ['96.bu1.a1', '96.bv1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5493, -1, 8498, -1, 3129, -1, 1685, -1], 'generators': [1179762397854127, 1822337812123926, 3846884234706384, 359890668365808], 'label': '768.1090131.48.co1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.co1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.co1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521613
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '48.cp1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.r1.a1', '24.bf1.a1', '24.br1.a1'], 'contains': ['96.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [3725, -1, 8196, -1, 2648, -1, 2400, -1], 'generators': [1558496692068486, 1822337812123926, 3846541581724590, 359890668365808], 'label': '768.1090131.48.cp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.cp1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.cp1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
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id: 68521614
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.a2', '16.b1.b1', '16.b1.b2'], 'contains': ['128.a1.a1', '128.b1.a1', '128.b1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [320, -1, 256, -1, 666, -1, 9468, -1], 'generators': [84307934393430, 4047630492624, 85621839894847], 'label': '768.1090131.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 68521615
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.c1.b1', '16.d1.a1', '16.e1.a1', '32.a1.a1', '32.c1.a1', '32.c1.b1'], 'contains': ['192.a1.a1', '256.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [641, -1, 2516, -1, 786, -1, 7825, -1], 'generators': [84307934393430, 1822337812123926, 359890668365808], 'label': '768.1090131.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 4, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521616
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b1.a1'], 'contains': ['192.t1.a1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [194, -1, 202, -1, 177, -1, 9659, -1], 'generators': [84307934393430, 1822038947023848, 795203061792528], 'label': '768.1090131.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.a1', 'old_label': '64.c1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68521617
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b1.b1'], 'contains': ['192.t1.b1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [194, -1, 1002, -1, 177, -1, 8169, -1], 'generators': [84307934393430, 2587548203909304, 5621224034334630], 'label': '768.1090131.64.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.b1', 'old_label': '64.c1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68521618
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b2.a1', '32.d1.a1', '32.d1.b1'], 'contains': ['192.t2.a1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [132, -1, 43, -1, 452, -1, 9593, -1], 'generators': [84307934393430, 359728823398326, 1821883084207920], 'label': '768.1090131.64.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '64.c2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521619
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b2.a2', '32.d1.a2', '32.d1.b2'], 'contains': ['192.t2.a2', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [132, -1, 126, -1, 452, -1, 9699, -1], 'generators': [84307934393430, 312321447414, 461960891286], 'label': '768.1090131.64.c2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '64.c2.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521621
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b2.b2', '32.d1.c2', '32.d1.d2'], 'contains': ['192.t2.b2', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [132, -1, 475, -1, 452, -1, 8428, -1], 'generators': [84307934393430, 1558054095215088, 3846242716609368], 'label': '768.1090131.64.c2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '64.c2.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 68521622
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 8, 'centralizer': '96.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1', '6.h1.a1', '6.h1.b1'], 'contains': ['24.br1.a1', '24.bu1.a1', '24.bw1.a1', '24.bw1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4567, 2441, 6505, 3052, 4362, 2192, 3713, 2613], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.a1.b1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
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id: 68521623
{'ambient': '768.1090131', 'aut_centralizer_order': 1024, 'aut_label': '96.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.o1.a1', '48.o1.b1', '48.p1.a1', '48.q1.a1', '48.r1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.g1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3806, 6018, 7143, 6738, 4566, 7843, 5029, 6987], 'generators': [1822337812123926, 359890668365808, 1], 'label': '768.1090131.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.a1.b1', '24.b1.a1'], 'normal_contains': ['192.a1.a1', '384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '6.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521624
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.i1.a1', '48.o1.a1'], 'contains': ['192.b1.a1', '192.c1.a1', '192.e1.a1', '192.h1.a1', '192.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2409, -1, 3296, -1, 4386, -1, 6539, -1], 'generators': [1822337812123926, 1, 461960891286], 'label': '768.1090131.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521625
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.d1.b1', '48.e1.b1', '48.f1.b1', '48.g1.a1', '48.i1.b1', '48.o1.b1'], 'contains': ['192.b1.a1', '192.c1.b1', '192.e1.b1', '192.h1.b1', '192.i1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2409, -1, 3978, -1, 4386, -1, 5634, -1], 'generators': [1822337812123926, 1, 3846242716609368], 'label': '768.1090131.96.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521626
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.i1.a1', '48.o1.a1'], 'contains': ['192.b1.a1', '192.c1.a1', '192.e2.a1', '192.h2.a1', '192.i2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2339, -1, 3328, -1, 2359, -1, 6584, -1], 'generators': [1, 461960891286, 795533260057254], 'label': '768.1090131.96.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '96.b2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521627
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.i1.b1', '48.o1.b1'], 'contains': ['192.b1.a1', '192.c1.b1', '192.e2.b1', '192.h2.b1', '192.i2.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2339, -1, 5061, -1, 2359, -1, 5813, -1], 'generators': [1, 3846242716609368, 795533260057254], 'label': '768.1090131.96.b2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '96.b2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521628
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.b1', '48.d1.a1', '48.d1.b1', '48.j1.a1', '48.k1.a1', '48.p1.a1'], 'contains': ['192.b1.a1', '192.d1.a1', '192.f1.a1', '192.j1.a1', '192.j1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4872, -1, 4384, -1, 5817, -1, 5504, -1], 'generators': [4047630492625, 4047630492624, 359890668365808], 'label': '768.1090131.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521629
{'ambient': '768.1090131', 'aut_centralizer_order': 512, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.q1.a1'], 'contains': ['192.b1.a1', '192.k1.a1', '192.l1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8187, -1, 8557, -1, 8340, -1, 1484, -1], 'generators': [1822337812123926, 3846697444535406, 1], 'label': '768.1090131.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521630
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.b1', '48.e1.a1', '48.e1.b1', '48.j1.a1', '48.l1.a1', '48.p1.a1'], 'contains': ['192.b1.a1', '192.m1.a1', '192.m1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5312, -1, 5934, -1, 6252, -1, 4909, -1], 'generators': [1821036378652951, 359890668365808, 1821036378652950], 'label': '768.1090131.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521631
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.m1.a1', '48.r1.a1'], 'contains': ['192.b1.a1', '192.n1.a1', '192.o1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4636, -1, 8608, -1, 5073, -1, 2623, -1], 'generators': [3846884234706384, 359890668365808, 1], 'label': '768.1090131.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521632
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.s1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.d1.a1', '192.p1.a1', '192.r1.a1', '192.r1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1440, -1, 1083, -1, 1761, -1, 8515, -1], 'generators': [4047630492625, 312321447414, 4047630492624], 'label': '768.1090131.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521633
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1'], 'contains': ['24.i1.a1', '24.k1.a1', '24.l1.a1', '24.bm1.a1', '24.bm1.b1', '24.bn1.a1', '24.bn1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3074, -1, 3301, -1, 4578, -1, 6400, -1], 'generators': [1822337812123926, 1179762397854126, 4047630492625, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521634
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.s1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.d1.a1', '192.p1.b1', '192.r1.c1', '192.r1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1440, -1, 1905, -1, 1761, -1, 7375, -1], 'generators': [4047630492625, 4047630492624, 1179562541714328], 'label': '768.1090131.96.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.g1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521635
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.s1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.s1.a1', '192.s1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [846, -1, 674, -1, 1234, -1, 8939, -1], 'generators': [4415227175929, 312321447414, 4415227175928], 'label': '768.1090131.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521636
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.s1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.s1.c1', '192.s1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [846, -1, 2387, -1, 1234, -1, 7107, -1], 'generators': [3844916347312825, 3844916347312824, 1179562541714328], 'label': '768.1090131.96.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.h1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521637
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.i1.a1'], 'contains': ['192.c1.a1', '192.q1.a1', '192.t1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [940, -1, 917, -1, 1036, -1, 8560, -1], 'generators': [312321447414, 1, 1821883084207920], 'label': '768.1090131.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '96.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68521641
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.b1', '48.i1.b1', '48.s1.b1'], 'contains': ['192.c1.b1', '192.q2.b1', '192.t2.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [659, -1, 2313, -1, 946, -1, 7007, -1], 'generators': [1, 1558054095215088, 5621224034334630], 'label': '768.1090131.96.i2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '96.i2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521642
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.b2', '48.i1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.q2.b2', '192.t2.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [659, -1, 2462, -1, 946, -1, 7206, -1], 'generators': [1, 1558054095215088, 3846242716609368], 'label': '768.1090131.96.i2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '96.i2.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521643
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.t1.a1', '48.t1.a2'], 'contains': ['192.e1.a1', '192.f1.a1', '192.p1.a1', '192.r1.a1', '192.r1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1994, -1, 1342, -1, 2269, -1, 8470, -1], 'generators': [312321447414, 356012206670569, 4047630492624], 'label': '768.1090131.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.j1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521644
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.i1.b1', '24.k1.b1', '24.l1.b1', '24.bm1.c1', '24.bm1.d1', '24.bn1.c1', '24.bn1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3074, -1, 5629, -1, 4578, -1, 5133, -1], 'generators': [1822337812123926, 4047630492625, 4047630492624, 1558428122581230, 359890668365808, 1179562541714328], 'label': '768.1090131.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521645
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.t1.b1', '48.t1.b2'], 'contains': ['192.e1.b1', '192.f1.a1', '192.p1.b1', '192.r1.c1', '192.r1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1994, -1, 1996, -1, 2269, -1, 7290, -1], 'generators': [356012206670569, 4047630492624, 1179562541714328], 'label': '768.1090131.96.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.j1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521646
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.t1.a1', '48.t1.a2'], 'contains': ['192.e1.a1', '192.s1.a1', '192.s1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1094, -1, 1009, -1, 1462, -1, 8659, -1], 'generators': [1820581643595246, 359728823398326, 796523194758631], 'label': '768.1090131.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.k1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521647
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.t1.b1', '48.t1.b2'], 'contains': ['192.e1.b1', '192.s1.c1', '192.s1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1094, -1, 2683, -1, 1462, -1, 6869, -1], 'generators': [2208813870141024, 5625108723085927, 4930927581391230], 'label': '768.1090131.96.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.k1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521648
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.t1.a1', '48.y1.a1'], 'contains': ['192.e1.a1', '192.e2.a1', '192.q1.a1', '192.q2.a1', '192.t2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1256, -1, 1305, -1, 1581, -1, 8301, -1], 'generators': [312321447414, 1822337812123927, 461960891286], 'label': '768.1090131.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.l1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521649
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.t1.a2', '48.y1.a1'], 'contains': ['192.e1.a1', '192.e2.a1', '192.q1.a1', '192.q2.a2', '192.t2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1256, -1, 1275, -1, 1581, -1, 8346, -1], 'generators': [312321447414, 1822337812123927, 360320459007774], 'label': '768.1090131.96.l1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.l1.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521650
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.t1.b1', '48.y1.b1'], 'contains': ['192.e1.b1', '192.e2.b1', '192.q1.b1', '192.q2.b2', '192.t2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1256, -1, 3111, -1, 1581, -1, 6719, -1], 'generators': [1822337812123927, 1558054095215088, 5621224034334630], 'label': '768.1090131.96.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.l1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521651
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.t1.b2', '48.y1.b1'], 'contains': ['192.e1.b1', '192.e2.b1', '192.q1.b1', '192.q2.b1', '192.t2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1256, -1, 3072, -1, 1581, -1, 6764, -1], 'generators': [1822337812123927, 1558054095215088, 3846242716609368], 'label': '768.1090131.96.l1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.l1.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521652
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.y1.a1'], 'contains': ['192.e1.a1', '192.e2.a1', '192.q1.a1', '192.q2.a1', '192.q2.a2', '192.t1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1370, -1, 1459, -1, 1671, -1, 8211, -1], 'generators': [312321447414, 1822337812123927, 1821883084207920], 'label': '768.1090131.96.l2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '96.l2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521653
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.l2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.y1.b1'], 'contains': ['192.e1.b1', '192.e2.b1', '192.q1.b1', '192.q2.b1', '192.q2.b2', '192.t1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1370, -1, 3024, -1, 1671, -1, 6449, -1], 'generators': [1822337812123927, 1558054095215088, 4934975208295326], 'label': '768.1090131.96.l2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '96.l2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521654
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.u1.a1', '48.u2.a1', '48.u2.b1', '48.v1.a1', '48.w1.a1', '48.y1.a1'], 'contains': ['192.e2.a1', '192.g1.a1', '192.h1.a1', '192.i1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2831, -1, 3606, -1, 4476, -1, 6359, -1], 'generators': [1822337812123926, 359890668365809, 461960891286], 'label': '768.1090131.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.m1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521655
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.i1.a1', '24.i1.b1', '24.m1.a1', '24.o1.a1', '24.s1.a1', '24.s1.b1', '24.v1.a1', '24.v1.b1', '24.be1.a1', '24.bo1.a1', '24.bo1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6637, -1, 5442, -1, 6665, -1, 4230, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521656
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.u1.b1', '48.u2.c1', '48.u2.d1', '48.v1.b1', '48.w1.a1', '48.y1.b1'], 'contains': ['192.e2.b1', '192.g1.a1', '192.h1.b1', '192.i1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2831, -1, 4648, -1, 4476, -1, 5420, -1], 'generators': [1822337812123926, 359890668365809, 3846242716609368], 'label': '768.1090131.96.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.m1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521657
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.m2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.x1.a1', '48.y1.a1'], 'contains': ['192.e1.a1', '192.e2.a1', '192.g1.a1', '192.h2.a1', '192.i2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2479, -1, 3391, -1, 2449, -1, 6404, -1], 'generators': [1822337812123927, 461960891286, 795533260057254], 'label': '768.1090131.96.m2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '96.m2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521658
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.m2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.x1.a1', '48.y1.b1'], 'contains': ['192.e1.b1', '192.e2.b1', '192.g1.a1', '192.h2.b1', '192.i2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2479, -1, 5091, -1, 2449, -1, 5768, -1], 'generators': [1822337812123927, 3846242716609368, 795533260057254], 'label': '768.1090131.96.m2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '96.m2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521659
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.u1.a1', '48.u1.b1', '48.u2.a1', '48.u2.c1', '48.z1.a1', '48.z2.a1'], 'contains': ['192.g1.a1', '192.j1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5200, -1, 5556, -1, 6138, -1, 4723, -1], 'generators': [1821036378652951, 4047630492624, 359890668365808], 'label': '768.1090131.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.n1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521660
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.u1.a1', '48.u1.b1', '48.u2.b1', '48.u2.d1', '48.z1.a1', '48.z2.b1'], 'contains': ['192.g1.a1', '192.j1.b1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5200, -1, 5718, -1, 6138, -1, 4843, -1], 'generators': [4047630492625, 359890668365808, 1821036378652950], 'label': '768.1090131.96.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.n1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521661
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.w1.a1', '48.z1.a1', '48.z2.a1', '48.z2.b1', '48.ba1.a1', '48.bb1.a1'], 'contains': ['192.g1.a1', '192.k1.a1', '192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8072, -1, 8657, -1, 8191, -1, 1409, -1], 'generators': [1822337812123926, 359890668365809, 3846697444535406], 'label': '768.1090131.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.o1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521662
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.x1.a1', '48.ba1.a1'], 'contains': ['192.g1.a1', '192.n1.a1', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4520, -1, 8707, -1, 4924, -1, 2549, -1], 'generators': [1822337812123927, 3846884234706384, 359890668365808], 'label': '768.1090131.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.p1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521663
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.w1.a1', '48.bc1.a1', '48.bc1.b1', '48.bd1.a1', '48.bd1.b1', '48.bq1.a1'], 'contains': ['192.h1.a1', '192.i1.b1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6208, -1, 5425, -1, 5980, -1, 3960, -1], 'generators': [1822337812123926, 461960891287, 3846242716609368], 'label': '768.1090131.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.q1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521664
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.w1.a1', '48.bc1.c1', '48.bc1.d1', '48.bd1.c1', '48.bd1.d1', '48.bq1.b1'], 'contains': ['192.h1.b1', '192.i1.a1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6208, -1, 5492, -1, 5980, -1, 4084, -1], 'generators': [1822337812123926, 3846242716609369, 461960891286], 'label': '768.1090131.96.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.q1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521665
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.x1.a1', '48.br1.a1'], 'contains': ['192.h2.a1', '192.i2.b1', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3220, -1, 6965, -1, 2691, -1, 5378, -1], 'generators': [312321447415, 3846242716609368, 795533260057254], 'label': '768.1090131.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.r1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521666
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.j1.a1', '24.j1.b1', '24.k1.a1', '24.k1.b1', '24.n1.a1', '24.p1.a1', '24.r1.a1', '24.w1.a1', '24.w1.b1', '24.z1.a1', '24.z1.b1', '24.bf1.a1', '24.bh1.a1', '24.bp1.a1', '24.br1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5063, -1, 7702, -1, 3469, -1, 2361, -1], 'generators': [1558496692068486, 1822337812123926, 312321447414, 359890668365808, 1, 3846242716609368], 'label': '768.1090131.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68521667
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.x1.a1', '48.br1.b1'], 'contains': ['192.h2.b1', '192.i2.a1', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3220, -1, 7562, -1, 2691, -1, 5462, -1], 'generators': [359890668365808, 461960891286, 1558054095215089], 'label': '768.1090131.96.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.r1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521668
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.u2.a1', '48.bc1.a1', '48.bd1.b1', '48.bg1.a1', '48.bh1.b1', '48.bs1.a1'], 'contains': ['192.h1.a1', '192.j1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5815, -1, 5329, -1, 6059, -1, 4238, -1], 'generators': [4047630492624, 359890668365808, 1820781140537905], 'label': '768.1090131.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.s1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521669
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.u2.b1', '48.bc1.b1', '48.bd1.a1', '48.bg1.b1', '48.bh1.a1', '48.bs1.a1'], 'contains': ['192.h1.a1', '192.j1.b1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5815, -1, 5370, -1, 6059, -1, 4317, -1], 'generators': [4253081604151, 359890668365808, 1821036378652950], 'label': '768.1090131.96.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.s1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521670
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.u2.c1', '48.bc1.c1', '48.bd1.d1', '48.bg1.a1', '48.bh1.b1', '48.bs1.b1'], 'contains': ['192.h1.b1', '192.j1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5815, -1, 5519, -1, 6059, -1, 4198, -1], 'generators': [4084267591005871, 4047630492624, 359890668365808], 'label': '768.1090131.96.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.s1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521671
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.u2.d1', '48.bc1.d1', '48.bd1.c1', '48.bg1.b1', '48.bh1.a1', '48.bs1.b1'], 'contains': ['192.h1.b1', '192.j1.b1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5815, -1, 5592, -1, 6059, -1, 4277, -1], 'generators': [1183459680839575, 359890668365808, 1821036378652950], 'label': '768.1090131.96.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.s1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521672
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.u1.a1', '48.bd1.a1', '48.bd1.b1', '48.bh1.a1', '48.bh1.b1', '48.bs1.a1'], 'contains': ['192.h1.a1', '192.j1.a1', '192.j1.b1', '192.p1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4427, -1, 4324, -1, 5499, -1, 4522, -1], 'generators': [4253081604151, 4047630492624, 359890668365808], 'label': '768.1090131.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.t1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521673
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.u1.b1', '48.bd1.c1', '48.bd1.d1', '48.bh1.a1', '48.bh1.b1', '48.bs1.b1'], 'contains': ['192.h1.b1', '192.j1.a1', '192.j1.b1', '192.p1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4427, -1, 5030, -1, 5499, -1, 4477, -1], 'generators': [1183459680839575, 4047630492624, 359890668365808], 'label': '768.1090131.96.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.t1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521803
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.i1.a1', '96.l2.a1', '96.be1.a1'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [966, -1, 1049, -1, 1378, -1, 8429, -1], 'generators': [312321447414, 1821883084207920], 'label': '768.1090131.192.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '192.t1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68521674
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.u1.a1', '48.bc1.a1', '48.bc1.b1', '48.bg1.a1', '48.bg1.b1', '48.bs1.a1'], 'contains': ['192.h1.a1', '192.m1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5112, -1, 6183, -1, 5697, -1, 3903, -1], 'generators': [359890668365808, 1820781140537905, 1821036378652950], 'label': '768.1090131.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.u1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521675
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.u1.b1', '48.bc1.c1', '48.bc1.d1', '48.bg1.a1', '48.bg1.b1', '48.bs1.b1'], 'contains': ['192.h1.b1', '192.m1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5112, -1, 6316, -1, 5697, -1, 4141, -1], 'generators': [4084267591005871, 359890668365808, 1821036378652950], 'label': '768.1090131.96.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.u1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521676
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.y1.a1', '48.be1.a1', '48.be1.b1', '48.bf1.a1', '48.bf1.b1', '48.bw1.a1'], 'contains': ['192.h2.a1', '192.i1.a1', '192.q1.a1', '192.q2.a1', '192.q2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1728, -1, 1613, -1, 2031, -1, 7978, -1], 'generators': [1822337812123926, 312321447415, 461960891286], 'label': '768.1090131.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.v1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521677
{'ambient': '768.1090131', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['384.f1.a1', '384.a1.a1', '384.b1.a1', '384.d1.a1', '384.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.h1.b1', '8.d1.b1', '8.d1.d1', '8.e1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1464, 2258, 937, 902, 1397, 2802, 6340, 2827], 'generators': [84307934393430, 1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '768.1090131', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68521678
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.x1.b1', '24.bs1.a1', '24.bs1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4736, -1, 4457, -1, 5807, -1, 5809, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 359890668365808, 4415227175928, 1179562541714328], 'label': '768.1090131.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521679
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.y1.b1', '48.be1.c1', '48.be1.d1', '48.bf1.c1', '48.bf1.d1', '48.bw1.b1'], 'contains': ['192.h2.b1', '192.i1.b1', '192.q1.b1', '192.q2.b1', '192.q2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1728, -1, 3358, -1, 2031, -1, 6016, -1], 'generators': [1822337812123926, 3846242716609368, 1558054095215089], 'label': '768.1090131.96.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.v1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521680
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.v2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.y1.a1', '48.bw1.a1'], 'contains': ['192.h1.a1', '192.h2.a1', '192.i2.a1', '192.q1.a1', '192.q2.a1', '192.q2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2077, -1, 1965, -1, 1941, -1, 7933, -1], 'generators': [312321447415, 461960891286, 795533260057254], 'label': '768.1090131.96.v2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '96.v2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521681
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.v2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.y1.b1', '48.bw1.b1'], 'contains': ['192.h1.b1', '192.h2.b1', '192.i2.b1', '192.q1.b1', '192.q2.b1', '192.q2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2077, -1, 3776, -1, 1941, -1, 5971, -1], 'generators': [3846242716609368, 795533260057254, 1558054095215089], 'label': '768.1090131.96.v2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '96.v2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521682
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.w1.a1', '48.bg1.a1', '48.bg1.b1', '48.bh1.a1', '48.bh1.b1', '48.bx1.a1'], 'contains': ['192.h1.a1', '192.h1.b1', '192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7441, -1, 6278, -1, 7173, -1, 3427, -1], 'generators': [1822337812123926, 3846697444535406, 3846242716609369], 'label': '768.1090131.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.w1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521683
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.x1.a1', '48.by1.a1'], 'contains': ['192.h2.a1', '192.h2.b1', '192.n1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3871, -1, 7624, -1, 2612, -1, 5338, -1], 'generators': [3846242716609369, 3846884234706384, 359890668365808], 'label': '768.1090131.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.x1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521684
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.u1.a1', '48.bc1.c1', '48.bd1.c1', '48.bi1.a1', '48.bj1.a1', '48.bz1.a1'], 'contains': ['192.i1.a1', '192.j1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5622, -1, 4006, -1, 5901, -1, 4643, -1], 'generators': [1822038947023848, 4047630492624, 359890668365808], 'label': '768.1090131.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.y1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521685
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.u1.a1', '48.bc1.d1', '48.bd1.d1', '48.bi1.b1', '48.bj1.b1', '48.bz1.b1'], 'contains': ['192.i1.a1', '192.j1.b1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5622, -1, 4412, -1, 5901, -1, 4763, -1], 'generators': [1821696294042054, 795533260057254, 85621839894847], 'label': '768.1090131.96.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.y1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521686
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.u1.b1', '48.bc1.a1', '48.bd1.a1', '48.bi1.a1', '48.bj1.a1', '48.bz1.c1'], 'contains': ['192.i1.b1', '192.j1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5622, -1, 4813, -1, 5901, -1, 4564, -1], 'generators': [4088283555510366, 4047630492624, 359890668365808], 'label': '768.1090131.96.y1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.y1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521687
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.u1.b1', '48.bc1.b1', '48.bd1.b1', '48.bi1.b1', '48.bj1.b1', '48.bz1.d1'], 'contains': ['192.i1.b1', '192.j1.b1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5622, -1, 4510, -1, 5901, -1, 4604, -1], 'generators': [795533260057254, 85621839894847, 4466613169859766], 'label': '768.1090131.96.y1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.y1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521688
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.u2.a1', '48.bd1.d1', '48.be1.a1', '48.bj1.a1', '48.bk1.a1', '48.bz1.a1'], 'contains': ['192.i1.a1', '192.j1.a1', '192.r1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2644, -1, 2807, -1, 4655, -1, 6629, -1], 'generators': [312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.z1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521689
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.e1.b1'], 'contains': ['24.l1.b1', '24.m1.a1', '24.x1.a1', '24.bs1.c1', '24.bs1.d1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4736, -1, 4780, -1, 5807, -1, 5030, -1], 'generators': [1822337812123926, 1562082513025344, 1562082513025345, 312321447414, 359890668365808, 1179562541714328], 'label': '768.1090131.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521690
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.u2.b1', '48.bd1.c1', '48.be1.b1', '48.bj1.b1', '48.bk1.b1', '48.bz1.b1'], 'contains': ['192.i1.a1', '192.j1.b1', '192.r1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2644, -1, 2838, -1, 4655, -1, 6674, -1], 'generators': [735925055088, 795533260057254, 85621839894847], 'label': '768.1090131.96.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.z1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521691
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.u2.c1', '48.bd1.b1', '48.be1.c1', '48.bj1.a1', '48.bk1.c1', '48.bz1.c1'], 'contains': ['192.i1.b1', '192.j1.a1', '192.r1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2644, -1, 3717, -1, 4655, -1, 5678, -1], 'generators': [4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.96.z1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.z1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521692
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.u2.d1', '48.bd1.a1', '48.be1.d1', '48.bj1.b1', '48.bk1.d1', '48.bz1.d1'], 'contains': ['192.i1.b1', '192.j1.b1', '192.r1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2644, -1, 3747, -1, 4655, -1, 5723, -1], 'generators': [1558054095215088, 795533260057254, 85621839894847], 'label': '768.1090131.96.z1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.z1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521693
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.u2.b1', '48.bc1.d1', '48.bf1.a1', '48.bi1.a1', '48.bl1.a1', '48.bz1.a1'], 'contains': ['192.i1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2924, -1, 3817, -1, 4775, -1, 6300, -1], 'generators': [312321447414, 359890668365808, 1821036378652950], 'label': '768.1090131.96.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.ba1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521694
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.u2.a1', '48.bc1.c1', '48.bf1.b1', '48.bi1.b1', '48.bl1.b1', '48.bz1.b1'], 'contains': ['192.i1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2924, -1, 3661, -1, 4775, -1, 6225, -1], 'generators': [1779365211990169, 735925055088, 795533260057254], 'label': '768.1090131.96.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.ba1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521695
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.u2.d1', '48.bc1.b1', '48.bf1.c1', '48.bi1.a1', '48.bl1.c1', '48.bz1.c1'], 'contains': ['192.i1.b1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2924, -1, 5194, -1, 4775, -1, 5281, -1], 'generators': [359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.96.ba1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.ba1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.c1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521696
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.u2.c1', '48.bc1.a1', '48.bf1.d1', '48.bi1.b1', '48.bl1.d1', '48.bz1.d1'], 'contains': ['192.i1.b1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2924, -1, 5144, -1, 4775, -1, 5207, -1], 'generators': [1779365211990169, 1558054095215088, 795533260057254], 'label': '768.1090131.96.ba1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.ba1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.d1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521697
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.v1.a1', '48.be1.a1', '48.bf1.a1', '48.bk1.b1', '48.bl1.b1', '48.ce1.a1'], 'contains': ['192.i1.a1', '192.s1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1636, -1, 1573, -1, 2150, -1, 8112, -1], 'generators': [85895741411455, 735925055088, 795533260057254], 'label': '768.1090131.96.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.bb1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521698
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.v1.a1', '48.be1.b1', '48.bf1.b1', '48.bk1.a1', '48.bl1.a1', '48.ce1.b1'], 'contains': ['192.i1.a1', '192.s1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1636, -1, 1653, -1, 2150, -1, 8038, -1], 'generators': [312321447414, 359890668365808, 4415227175928], 'label': '768.1090131.96.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.bb1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521699
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.v1.b1', '48.be1.c1', '48.bf1.c1', '48.bk1.d1', '48.bl1.d1', '48.ce1.c1'], 'contains': ['192.i1.b1', '192.s1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1636, -1, 2912, -1, 2150, -1, 6076, -1], 'generators': [3824964916138807, 1558054095215088, 795533260057254], 'label': '768.1090131.96.bb1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.bb1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521700
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.m1.a1', '24.q1.a1', '24.bi1.a1', '24.bt1.a1', '24.bt1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8121, -1, 7487, -1, 7694, -1, 1660, -1], 'generators': [1822337812123926, 312321447414, 1562469074861448, 359890668365808, 1179562541714328, 1562469074861449], 'label': '768.1090131.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521701
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.v1.b1', '48.be1.d1', '48.bf1.d1', '48.bk1.c1', '48.bl1.c1', '48.ce1.d1'], 'contains': ['192.i1.b1', '192.s1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1636, -1, 2984, -1, 2150, -1, 6150, -1], 'generators': [359890668365808, 3844916347312824, 1179562541714328], 'label': '768.1090131.96.bb1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.bb1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521702
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.p1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.w1.a1', '48.bi1.a1', '48.bi1.b1', '48.bj1.a1', '48.bj1.b1', '48.cf1.a1'], 'contains': ['192.i1.a1', '192.i1.b1', '192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7117, -1, 4949, -1, 6591, -1, 4356, -1], 'generators': [1822337812123926, 461960891286, 3846242716609368], 'label': '768.1090131.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bc1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521703
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.x1.a1', '48.cg1.a1'], 'contains': ['192.i2.a1', '192.i2.b1', '192.n1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [3282, -1, 6909, -1, 2533, -1, 5547, -1], 'generators': [359890668365808, 735925055088, 3846242716609368], 'label': '768.1090131.96.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.bd1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521704
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.i1.a1', '48.y1.a1', '48.bk1.a1', '48.bk1.b1', '48.bl1.a1', '48.bl1.b1'], 'contains': ['192.i1.a1', '192.i2.a1', '192.t1.a1', '192.t2.a1', '192.t2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1543, -1, 1371, -1, 1851, -1, 8256, -1], 'generators': [1822337812123926, 312321447414, 461960891286], 'label': '768.1090131.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.be1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521705
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.i1.b1', '48.y1.b1', '48.bk1.c1', '48.bk1.d1', '48.bl1.c1', '48.bl1.d1'], 'contains': ['192.i1.b1', '192.i2.b1', '192.t1.b1', '192.t2.b1', '192.t2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1543, -1, 2868, -1, 1851, -1, 6494, -1], 'generators': [1822337812123926, 1558054095215088, 3846242716609368], 'label': '768.1090131.96.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.be1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521706
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.z2.a1', '48.bc1.a1', '48.bc1.c1', '48.bd1.b1', '48.bd1.d1', '48.ch1.a1'], 'contains': ['192.j1.a1', '192.k1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6366, -1, 6546, -1, 6448, -1, 3754, -1], 'generators': [1183572256704511, 4047630492624, 359890668365808], 'label': '768.1090131.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bf1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521707
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.z2.b1', '48.bc1.b1', '48.bc1.d1', '48.bd1.a1', '48.bd1.c1', '48.ch1.a1'], 'contains': ['192.j1.b1', '192.k1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6366, -1, 7053, -1, 6448, -1, 3829, -1], 'generators': [359890668365808, 4084074586373095, 1821036378652950], 'label': '768.1090131.96.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bf1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521708
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.z1.a1', '48.bg1.a1', '48.bh1.a1', '48.bi1.a1', '48.bj1.a1', '48.ci1.a1'], 'contains': ['192.j1.a1', '192.l1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7534, -1, 7103, -1, 7311, -1, 3124, -1], 'generators': [4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bg1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521709
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.j1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.z1.a1', '48.bg1.b1', '48.bh1.b1', '48.bi1.b1', '48.bj1.b1', '48.ci1.b1'], 'contains': ['192.j1.b1', '192.l1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7534, -1, 7003, -1, 7311, -1, 3313, -1], 'generators': [1558328613944424, 795533260057254, 85621839894847], 'label': '768.1090131.96.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bg1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521710
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.z1.a1', '48.bd1.a1', '48.bd1.b1', '48.bd1.c1', '48.bd1.d1', '48.ch1.a1'], 'contains': ['192.j1.a1', '192.j1.b1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6631, -1, 5452, -1, 6670, -1, 4000, -1], 'generators': [4047630492624, 359890668365808, 4084074586373095], 'label': '768.1090131.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bh1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521711
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '24.j1.a1', '24.j1.b1', '24.m1.a1', '24.p1.a1', '24.y1.a1', '24.y1.b1', '24.bg1.a1', '24.bj1.a1', '24.bq1.a1', '24.bu1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7398, -1, 7976, -1, 7011, -1, 1911, -1], 'generators': [1822337812123926, 1558428122581230, 359890668365808, 1, 461960891286, 3846242716609368], 'label': '768.1090131.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521712
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.z2.a1', '48.bh1.b1', '48.bj1.a1', '48.bm1.a1', '48.bn1.a1', '48.ci1.a1'], 'contains': ['192.j1.a1', '192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8512, -1, 8145, -1, 8501, -1, 1541, -1], 'generators': [4047630492624, 4088009123503584, 359890668365808], 'label': '768.1090131.96.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.bi1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521713
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.k1.a1', '48.z2.b1', '48.bh1.a1', '48.bj1.b1', '48.bm1.b1', '48.bn1.b1', '48.ci1.b1'], 'contains': ['192.j1.b1', '192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8512, -1, 8171, -1, 8501, -1, 1580, -1], 'generators': [4466413379048430, 795533260057254, 85621839894847], 'label': '768.1090131.96.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.bi1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521714
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.z1.a1', '48.bc1.a1', '48.bc1.b1', '48.bc1.c1', '48.bc1.d1', '48.ch1.a1'], 'contains': ['192.k1.a1', '192.m1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6694, -1, 7170, -1, 6749, -1, 3641, -1], 'generators': [1183572256704511, 359890668365808, 1821036378652950], 'label': '768.1090131.96.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.bj1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521715
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bk1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.ba1.a1', '48.cj1.a1'], 'contains': ['192.k1.a1', '192.n1.a1', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8406, -1, 9096, -1, 7962, -1, 1199, -1], 'generators': [3846884234706384, 359890668365808, 1558496692068487], 'label': '768.1090131.96.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.p1.a1', 'old_label': '96.bk1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521716
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.z2.b1', '48.bg1.b1', '48.bi1.a1', '48.bo1.a1', '48.bp1.a1', '48.ci1.a1'], 'contains': ['192.l1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8675, -1, 8745, -1, 8627, -1, 1278, -1], 'generators': [4088009123503584, 359890668365808, 1821036378652950], 'label': '768.1090131.96.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.bl1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521717
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bl1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.l1.a1', '48.z2.a1', '48.bg1.a1', '48.bi1.b1', '48.bo1.b1', '48.bp1.b1', '48.ci1.b1'], 'contains': ['192.l1.a1', '192.m1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8675, -1, 8331, -1, 8627, -1, 1238, -1], 'generators': [4466413379048430, 1779365211990169, 795533260057254], 'label': '768.1090131.96.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.bl1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521718
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bm1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.ba1.a1', '48.bm1.a1', '48.bm1.b1', '48.bo1.a1', '48.bo1.b1', '48.cl1.a1'], 'contains': ['192.l1.a1', '192.n1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9032, -1, 9430, -1, 8965, -1, 593, -1], 'generators': [1179762397854126, 3846541581724590, 795533260057254], 'label': '768.1090131.96.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.bm1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521719
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bn1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.m1.a1', '48.ba1.a1', '48.bn1.a1', '48.bn1.b1', '48.bp1.a1', '48.bp1.b1', '48.cm1.a1'], 'contains': ['192.l1.a1', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9161, -1, 9457, -1, 9044, -1, 554, -1], 'generators': [1822337812123926, 3846697444535406, 1558428122581231], 'label': '768.1090131.96.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.bn1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521720
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.bb1.a1', '48.bm1.b1', '48.bn1.a1', '48.bo1.b1', '48.bp1.a1', '48.cn1.a1'], 'contains': ['192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9525, -1, 9673, -1, 9588, -1, 273, -1], 'generators': [4466413379048430, 3825182759822761, 795533260057254], 'label': '768.1090131.96.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.bo1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521721
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.bo1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.bb1.a1', '48.bm1.a1', '48.bn1.b1', '48.bo1.a1', '48.bp1.b1', '48.cn1.b1'], 'contains': ['192.l1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9525, -1, 9718, -1, 9588, -1, 376, -1], 'generators': [4088009123503584, 359890668365808, 3845532940242606], 'label': '768.1090131.96.bo1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.bo1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bo1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521722
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.f1.a1', '24.i1.a1', '24.l1.a1', '24.t1.a1', '24.t1.b1', '24.bb1.a1', '24.bb1.b1', '24.bv1.a1', '24.bv1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1446, -1, 2218, -1, 2047, -1, 7628, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521723
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.bq1.a1', '48.br1.a1', '48.bs1.a1', '48.bt1.a1', '48.bu1.a1', '48.bv1.a1', '48.bw1.a1', '48.bx1.a1', '48.by1.a1'], 'contains': ['192.a1.a1', '192.h1.a1', '192.h2.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4357, -1, 6937, -1, 4145, -1, 2869, -1], 'generators': [1822337812123926, 461960891287, 359890668365808], 'label': '768.1090131.96.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bp1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521724
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bp1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.bq1.b1', '48.br1.b1', '48.bs1.b1', '48.bt1.b1', '48.bu1.b1', '48.bv1.b1', '48.bw1.b1', '48.bx1.a1', '48.by1.a1'], 'contains': ['192.a1.a1', '192.h1.b1', '192.h2.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4357, -1, 7775, -1, 4145, -1, 2824, -1], 'generators': [1822337812123926, 3846242716609369, 359890668365808], 'label': '768.1090131.96.bp1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bp1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bp1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521725
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.o1.a1', '48.bq1.b1', '48.br1.b1', '48.bw1.a1', '48.bz1.a1', '48.bz1.b1', '48.ca1.a1', '48.cb1.a1', '48.cc1.a1', '48.cd1.a1', '48.ce1.a1', '48.ce1.b1', '48.cf1.a1', '48.cg1.a1'], 'contains': ['192.a1.a1', '192.i1.a1', '192.i2.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3089, -1, 4354, -1, 3849, -1, 5589, -1], 'generators': [1822337812123926, 359890668365808, 461960891286], 'label': '768.1090131.96.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bq1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521726
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bq1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.o1.b1', '48.bq1.a1', '48.br1.a1', '48.bw1.b1', '48.bz1.c1', '48.bz1.d1', '48.ca1.b1', '48.cb1.b1', '48.cc1.b1', '48.cd1.b1', '48.ce1.c1', '48.ce1.d1', '48.cf1.a1', '48.cg1.a1'], 'contains': ['192.a1.a1', '192.i1.b1', '192.i2.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3089, -1, 5894, -1, 3849, -1, 4042, -1], 'generators': [1822337812123926, 359890668365808, 3846242716609368], 'label': '768.1090131.96.bq1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bq1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bq1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521727
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '48.p1.a1', '48.bs1.a1', '48.bs1.b1', '48.bz1.a1', '48.bz1.c1', '48.ch1.a1', '48.ci1.a1'], 'contains': ['192.a1.a1', '192.j1.a1', '192.m1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4033, -1, 6883, -1, 5583, -1, 4395, -1], 'generators': [1822337812123926, 4047630492624, 359890668365808], 'label': '768.1090131.96.br1.a1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.br1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521728
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '96.br1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '48.p1.a1', '48.bs1.a1', '48.bs1.b1', '48.bz1.b1', '48.bz1.d1', '48.ch1.a1', '48.ci1.b1'], 'contains': ['192.a1.a1', '192.j1.b1', '192.m1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4033, -1, 6252, -1, 5583, -1, 4435, -1], 'generators': [1822337812123926, 359890668365808, 85621839894847], 'label': '768.1090131.96.br1.b1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.br1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.br1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521729
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.bs1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.bq1.a1', '48.bq1.b1', '48.bt1.a1', '48.bt1.b1', '48.ca1.a1', '48.ca1.b1', '48.ch1.a1', '48.cj1.a1', '48.ck1.a1'], 'contains': ['192.a1.a1', '192.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6110, -1, 8269, -1, 5222, -1, 2068, -1], 'generators': [1822337812123926, 3846697444535407, 359890668365808], 'label': '768.1090131.96.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bs1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521730
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '96.bt1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.q1.a1', '48.bu1.a1', '48.bu1.b1', '48.bx1.a1', '48.cb1.a1', '48.cb1.b1', '48.cf1.a1', '48.ci1.a1', '48.ci1.b1', '48.ck1.a1', '48.cl1.a1', '48.cm1.a1', '48.cn1.a1', '48.cn1.b1'], 'contains': ['192.a1.a1', '192.l1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8318, -1, 9058, -1, 7848, -1, 1335, -1], 'generators': [1822337812123926, 3846697444535406, 359890668365808], 'label': '768.1090131.96.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bt1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68521731
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bu1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.bt1.a1', '48.bt1.b1', '48.bv1.a1', '48.bv1.b1', '48.by1.a1', '48.cb1.a1', '48.cb1.b1', '48.cc1.a1', '48.cc1.b1', '48.cg1.a1', '48.cj1.a1', '48.cl1.a1', '48.co1.a1', '48.cp1.a1'], 'contains': ['192.a1.a1', '192.n1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4779, -1, 8458, -1, 3730, -1, 2273, -1], 'generators': [1822337812123926, 3846884234706384, 359890668365808], 'label': '768.1090131.96.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.bu1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521732
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '96.bv1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.r1.a1', '48.br1.a1', '48.br1.b1', '48.bu1.a1', '48.bu1.b1', '48.bv1.a1', '48.bv1.b1', '48.ca1.a1', '48.ca1.b1', '48.cd1.a1', '48.cd1.b1', '48.cj1.a1', '48.cm1.a1', '48.co1.a1'], 'contains': ['192.a1.a1', '192.o1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5428, -1, 8508, -1, 4266, -1, 2198, -1], 'generators': [1822337812123926, 3846541581724591, 359890668365808], 'label': '768.1090131.96.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.bv1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521733
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.d1.a1'], 'contains': ['24.a1.b1', '24.e1.b1', '24.f1.b1', '24.i1.b1', '24.l1.b1', '24.t1.c1', '24.t1.d1', '24.bb1.c1', '24.bb1.d1', '24.bv1.c1', '24.bv1.d1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1446, -1, 3845, -1, 2047, -1, 5929, -1], 'generators': [1822337812123926, 4047630492625, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.h1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521734
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.t1.a1', '48.be1.a1'], 'contains': ['192.q2.a1', '192.r1.a1', '192.s1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 972, -1, 1348, -1, 8716, -1], 'generators': [1820581643595247, 4047630492624, 359728823398326], 'label': '768.1090131.96.bw1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bw1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521735
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a2', '48.t1.a2', '48.be1.a1'], 'contains': ['192.q2.a2', '192.r1.a1', '192.s1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 945, -1, 1348, -1, 8816, -1], 'generators': [4415227175929, 312321447414, 4047630492624], 'label': '768.1090131.96.bw1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bw1.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521736
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a1', '48.t1.a1', '48.be1.b1'], 'contains': ['192.q2.a1', '192.r1.b1', '192.s1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 1176, -1, 1348, -1, 8602, -1], 'generators': [4047630492625, 1820581643595246, 359728823398326], 'label': '768.1090131.96.bw1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bw1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521737
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.a2', '48.t1.a2', '48.be1.b1'], 'contains': ['192.q2.a2', '192.r1.b1', '192.s1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 1114, -1, 1348, -1, 8777, -1], 'generators': [4047630492625, 312321447414, 4415227175928], 'label': '768.1090131.96.bw1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bw1.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521738
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.b1', '48.t1.b2', '48.be1.c1'], 'contains': ['192.q2.b1', '192.r1.c1', '192.s1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 2537, -1, 1348, -1, 6926, -1], 'generators': [4930927581391231, 4047630492624, 2208813870141024], 'label': '768.1090131.96.bw1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bw1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521739
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.b2', '48.t1.b1', '48.be1.c1'], 'contains': ['192.q2.b2', '192.r1.c1', '192.s1.c1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 2500, -1, 1348, -1, 6965, -1], 'generators': [3844916347312825, 4047630492624, 1179562541714328], 'label': '768.1090131.96.bw1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bw1.c2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.c2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521740
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.b1', '48.t1.b2', '48.be1.d1'], 'contains': ['192.q2.b1', '192.r1.d1', '192.s1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 2626, -1, 1348, -1, 7050, -1], 'generators': [4047630492625, 2208813870141024, 4930927581391230], 'label': '768.1090131.96.bw1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bw1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521741
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bw1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.s1.b2', '48.t1.b1', '48.be1.d1'], 'contains': ['192.q2.b2', '192.r1.d1', '192.s1.d1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1005, -1, 2588, -1, 1348, -1, 7164, -1], 'generators': [4047630492625, 3844916347312824, 1179562541714328], 'label': '768.1090131.96.bw1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bw1.d2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bw1.d2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521742
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a1', '48.s1.a1', '48.t1.a2', '48.bk1.a1'], 'contains': ['192.r1.a1', '192.s1.b1', '192.t2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 712, -1, 1120, -1, 9083, -1], 'generators': [4047630492624, 359728823398326, 1821883084207920], 'label': '768.1090131.96.bx1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bx1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521743
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.a2', '48.s1.a2', '48.t1.a1', '48.bk1.a1'], 'contains': ['192.r1.a1', '192.s1.b1', '192.t2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 779, -1, 1120, -1, 9122, -1], 'generators': [312321447414, 4047630492624, 461960891286], 'label': '768.1090131.96.bx1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bx1.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521744
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.b1', '24.j1.b1', '24.k1.b1', '24.m1.a1', '24.n1.a1', '24.ba1.a1', '24.bc1.b1', '24.bd1.b1', '24.bk1.a1', '24.bl1.a1', '24.bw1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4181, -1, 6422, -1, 3921, -1, 3076, -1], 'generators': [1822337812123926, 359890668365808, 1, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521745
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b1', '48.s1.a1', '48.t1.a2', '48.bk1.b1'], 'contains': ['192.r1.b1', '192.s1.a1', '192.t2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 606, -1, 1120, -1, 9162, -1], 'generators': [359728823398326, 85621839894847, 1821883084207920], 'label': '768.1090131.96.bx1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bx1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521746
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.b2', '48.s1.a2', '48.t1.a1', '48.bk1.b1'], 'contains': ['192.r1.b1', '192.s1.a1', '192.t2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 753, -1, 1120, -1, 9201, -1], 'generators': [312321447414, 461960891286, 85621839894847], 'label': '768.1090131.96.bx1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.bx1.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521747
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c1', '48.s1.b1', '48.t1.b1', '48.bk1.c1'], 'contains': ['192.r1.c1', '192.s1.d1', '192.t2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 2100, -1, 1120, -1, 7248, -1], 'generators': [4047630492624, 3437629559701230, 4934975208295326], 'label': '768.1090131.96.bx1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bx1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.c1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521748
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.c2', '48.s1.b2', '48.t1.b2', '48.bk1.c1'], 'contains': ['192.r1.c1', '192.s1.d1', '192.t2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 2218, -1, 1120, -1, 7417, -1], 'generators': [4047630492624, 1558054095215088, 3846242716609368], 'label': '768.1090131.96.bx1.c2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bx1.c2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.c2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521749
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d1', '48.s1.b1', '48.t1.b1', '48.bk1.d1'], 'contains': ['192.r1.d1', '192.s1.c1', '192.t2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 2051, -1, 1120, -1, 7333, -1], 'generators': [3437629559701230, 85621839894847, 4934975208295326], 'label': '768.1090131.96.bx1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bx1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.d1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521750
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '96.bx1', 'aut_quo_index': None, 'aut_stab_index': 192, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.d1.d2', '48.s1.b2', '48.t1.b2', '48.bk1.d1'], 'contains': ['192.r1.d1', '192.s1.c1', '192.t2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [757, -1, 2127, -1, 1120, -1, 7457, -1], 'generators': [1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.96.bx1.d2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.bx1.d2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bx1.d2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68521751
{'ambient': '768.1090131', 'aut_centralizer_order': 48, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.b2.a1', '32.b2.a2', '32.b2.b1', '32.b2.b2', '64.a1.a1'], 'contains': ['256.a1.a1', '384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [101, -1, 255, -1, 626, -1, 9349, -1], 'generators': [84307934393430, 84307934393431], 'label': '768.1090131.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521752
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.a1', '32.d1.a1', '32.d1.a2', '32.d1.c1', '32.d1.c2', '64.a1.a1'], 'contains': ['256.a1.a1', '384.f1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [385, -1, 360, -1, 726, -1, 9252, -1], 'generators': [84307934393430, 4047630492624], 'label': '768.1090131.128.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.b1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521753
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '128.b1', 'aut_quo_index': None, 'aut_stab_index': 128, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.c1.b1', '32.d1.b1', '32.d1.b2', '32.d1.d1', '32.d1.d2', '64.a1.a1'], 'contains': ['256.a1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [385, -1, 386, -1, 726, -1, 9297, -1], 'generators': [84307934393430, 85621839894847], 'label': '768.1090131.128.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.b1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.b1.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521754
{'ambient': '768.1090131', 'aut_centralizer_order': 1024, 'aut_label': '192.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.a1.a1', '96.bp1.a1', '96.bp1.b1', '96.bq1.a1', '96.bq1.b1', '96.br1.a1', '96.br1.b1', '96.bs1.a1', '96.bt1.a1', '96.bu1.a1', '96.bv1.a1'], 'contains': ['384.c1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4239, 4452, 6937, 5586, 4327, 5967, 4042, 5529], 'generators': [1822337812123926, 359890668365808], 'label': '768.1090131.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': -192, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.a1.b1', '48.b1.a1', '96.a1.a1'], 'normal_contains': ['768.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521755
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.j1.a1', '24.k1.a1', '24.m1.a1', '24.n1.a1', '24.ba1.b1', '24.bc1.a1', '24.bd1.a1', '24.bk1.b1', '24.bl1.b1', '24.bw1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4181, -1, 6044, -1, 3921, -1, 3858, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 1, 461960891286, 3846242716609368], 'label': '768.1090131.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521756
{'ambient': '768.1090131', 'aut_centralizer_order': 2048, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b2.a1', '96.b2.b1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1'], 'contains': ['384.a1.a1', '384.b1.a1', '384.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3944, -1, 5148, -1, 4824, -1, 5569, -1], 'generators': [1822337812123926, 1], 'label': '768.1090131.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521757
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.b2.a1', '96.g1.a1', '96.h1.a1', '96.i1.a1', '96.i2.a1', '96.i2.a2'], 'contains': ['384.a1.a1', '384.d1.a1', '384.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1305, -1, 985, -1, 1641, -1, 8384, -1], 'generators': [1, 461960891286], 'label': '768.1090131.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521758
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.b2.b1', '96.g1.b1', '96.h1.b1', '96.i1.b1', '96.i2.b1', '96.i2.b2'], 'contains': ['384.a1.a1', '384.d1.b1', '384.e1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1305, -1, 2719, -1, 1641, -1, 6923, -1], 'generators': [1, 3846242716609368], 'label': '768.1090131.192.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.c1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521759
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.c1.a1', '96.g1.a1', '96.g1.b1'], 'contains': ['384.a1.a1', '384.f1.a1', '384.f1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1773, -1, 1576, -1, 1910, -1, 7828, -1], 'generators': [4047630492625, 4047630492624], 'label': '768.1090131.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '192.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521760
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.j1.a1', '96.k1.a1', '96.l1.a1', '96.l1.a2', '96.l2.a1', '96.m2.a1'], 'contains': ['384.b1.a1', '384.d1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1844, -1, 1606, -1, 2090, -1, 7783, -1], 'generators': [1822337812123927, 461960891286], 'label': '768.1090131.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.e1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521761
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.j1.b1', '96.k1.b1', '96.l1.b1', '96.l1.b2', '96.l2.b1', '96.m2.b1'], 'contains': ['384.b1.a1', '384.d1.b1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1844, -1, 3114, -1, 2090, -1, 6743, -1], 'generators': [1822337812123927, 3846242716609368], 'label': '768.1090131.192.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.e1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521762
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.e2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.l1.a1', '96.l1.a2', '96.l2.a1', '96.m1.a1', '96.m2.a1'], 'contains': ['384.b1.a1', '384.d1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1957, -1, 1666, -1, 2180, -1, 7693, -1], 'generators': [359890668365809, 461960891286], 'label': '768.1090131.192.e2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '192.e2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521763
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.e2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.l1.b1', '96.l1.b2', '96.l2.b1', '96.m1.b1', '96.m2.b1'], 'contains': ['384.b1.a1', '384.d1.b1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1957, -1, 3301, -1, 2180, -1, 6449, -1], 'generators': [359890668365809, 3846242716609368], 'label': '768.1090131.192.e2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '192.e2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521764
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.j1.a1', '96.j1.b1'], 'contains': ['384.b1.a1', '384.f1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2804, -1, 1819, -1, 2539, -1, 7519, -1], 'generators': [356012206670569, 4047630492624], 'label': '768.1090131.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '192.f1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521765
{'ambient': '768.1090131', 'aut_centralizer_order': 1024, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.m1.a1', '96.m1.b1', '96.m2.a1', '96.m2.b1', '96.n1.a1', '96.n1.b1', '96.o1.a1', '96.p1.a1'], 'contains': ['384.b1.a1', '384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3855, -1, 5332, -1, 4566, -1, 5029, -1], 'generators': [1822337812123926, 359890668365809], 'label': '768.1090131.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '192.g1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521766
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1', '24.u1.a1', '24.u1.b1', '24.by1.a1', '24.by1.b1', '24.bz1.a1', '24.bz1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9248, -1, 9463, -1, 8867, -1, 546, -1], 'generators': [1558496692068486, 1822337812123926, 4047630492625, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521767
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.m1.a1', '96.q1.a1', '96.s1.a1', '96.s1.b1', '96.t1.a1', '96.u1.a1', '96.v2.a1', '96.w1.a1', '96.bp1.a1'], 'contains': ['384.c1.a1', '384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4358, -1, 4828, -1, 4734, -1, 4429, -1], 'generators': [1822337812123926, 461960891287], 'label': '768.1090131.192.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '192.h1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521768
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.m1.b1', '96.q1.b1', '96.s1.c1', '96.s1.d1', '96.t1.b1', '96.u1.b1', '96.v2.b1', '96.w1.a1', '96.bp1.b1'], 'contains': ['384.c1.a1', '384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4358, -1, 5271, -1, 4734, -1, 4377, -1], 'generators': [1822337812123926, 3846242716609369], 'label': '768.1090131.192.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '192.h1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521769
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.h2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.m2.a1', '96.r1.a1', '96.v1.a1', '96.v2.a1', '96.x1.a1', '96.bp1.a1'], 'contains': ['384.c1.a1', '384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2604, -1, 3413, -1, 2449, -1, 6404, -1], 'generators': [461960891287, 795533260057254], 'label': '768.1090131.192.h2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '192.h2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521804
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.b1', '96.i1.b1', '96.l2.b1', '96.be1.b1'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [966, -1, 2773, -1, 1378, -1, 6878, -1], 'generators': [1558054095215088, 4934975208295326], 'label': '768.1090131.192.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '192.t1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68521770
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.h2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.m2.b1', '96.r1.b1', '96.v1.b1', '96.v2.b1', '96.x1.a1', '96.bp1.b1'], 'contains': ['384.c1.a1', '384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2604, -1, 5302, -1, 2449, -1, 5746, -1], 'generators': [3846242716609369, 795533260057254], 'label': '768.1090131.192.h2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '192.h2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521771
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.m1.a1', '96.q1.b1', '96.v1.a1', '96.y1.a1', '96.y1.b1', '96.z1.a1', '96.z1.b1', '96.ba1.a1', '96.ba1.b1', '96.bb1.a1', '96.bb1.b1', '96.bc1.a1', '96.be1.a1', '96.bq1.a1'], 'contains': ['384.c1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2733, -1, 3271, -1, 4476, -1, 6494, -1], 'generators': [1822337812123926, 461960891286], 'label': '768.1090131.192.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '192.i1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521772
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.m1.b1', '96.q1.a1', '96.v1.b1', '96.y1.c1', '96.y1.d1', '96.z1.c1', '96.z1.d1', '96.ba1.c1', '96.ba1.d1', '96.bb1.c1', '96.bb1.d1', '96.bc1.a1', '96.be1.b1', '96.bq1.b1'], 'contains': ['384.c1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2733, -1, 4510, -1, 4476, -1, 5420, -1], 'generators': [1822337812123926, 3846242716609368], 'label': '768.1090131.192.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '192.i1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521773
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.i2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.m2.a1', '96.r1.b1', '96.v2.a1', '96.bd1.a1', '96.be1.a1', '96.bq1.a1'], 'contains': ['384.c1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2442, -1, 3384, -1, 2359, -1, 6539, -1], 'generators': [461960891286, 795533260057254], 'label': '768.1090131.192.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '192.i2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521774
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.i2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.m2.b1', '96.r1.a1', '96.v2.b1', '96.bd1.a1', '96.be1.b1', '96.bq1.b1'], 'contains': ['384.c1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2442, -1, 4859, -1, 2359, -1, 5791, -1], 'generators': [3846242716609368, 795533260057254], 'label': '768.1090131.192.i2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '192.i2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521775
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.n1.a1', '96.s1.a1', '96.s1.c1', '96.t1.a1', '96.t1.b1', '96.y1.a1', '96.y1.c1', '96.z1.a1', '96.z1.c1', '96.bf1.a1', '96.bg1.a1', '96.bh1.a1', '96.bi1.a1', '96.br1.a1'], 'contains': ['384.c1.a1', '384.f1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4997, -1, 5010, -1, 5901, -1, 4477, -1], 'generators': [4047630492624, 359890668365808], 'label': '768.1090131.192.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.j1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521776
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.n1.b1', '96.s1.b1', '96.s1.d1', '96.t1.a1', '96.t1.b1', '96.y1.b1', '96.y1.d1', '96.z1.b1', '96.z1.d1', '96.bf1.b1', '96.bg1.b1', '96.bh1.a1', '96.bi1.b1', '96.br1.b1'], 'contains': ['384.c1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4997, -1, 5119, -1, 5901, -1, 4522, -1], 'generators': [795533260057254, 85621839894847], 'label': '768.1090131.192.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.j1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521777
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.o1.a1', '24.q1.a1', '24.bx1.a1', '24.bx1.b1', '24.ca1.a1', '24.ca1.b1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7942, -1, 8933, -1, 7922, -1, 1201, -1], 'generators': [1822337812123926, 4047630492625, 3846697444535406, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68521778
{'ambient': '768.1090131', 'aut_centralizer_order': 512, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.o1.a1', '96.q1.a1', '96.q1.b1', '96.bf1.a1', '96.bf1.b1', '96.bh1.a1', '96.bj1.a1', '96.bk1.a1', '96.bs1.a1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6629, -1, 7053, -1, 6670, -1, 3754, -1], 'generators': [1822337812123926, 3846697444535407], 'label': '768.1090131.192.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '192.k1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521779
{'ambient': '768.1090131', 'aut_centralizer_order': 512, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.o1.a1', '96.w1.a1', '96.bc1.a1', '96.bg1.a1', '96.bg1.b1', '96.bi1.a1', '96.bi1.b1', '96.bl1.a1', '96.bl1.b1', '96.bm1.a1', '96.bn1.a1', '96.bo1.a1', '96.bo1.b1', '96.bt1.a1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8252, -1, 8573, -1, 8265, -1, 1447, -1], 'generators': [1822337812123926, 3846697444535406], 'label': '768.1090131.192.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '192.l1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521780
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.n1.b1', '96.s1.b1', '96.s1.d1', '96.u1.a1', '96.u1.b1', '96.y1.a1', '96.y1.c1', '96.ba1.a1', '96.ba1.c1', '96.bf1.b1', '96.bg1.a1', '96.bj1.a1', '96.bl1.a1', '96.br1.a1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5570, -1, 5906, -1, 6098, -1, 4320, -1], 'generators': [359890668365808, 1821036378652950], 'label': '768.1090131.192.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.m1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521781
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.e1.a1', '96.n1.a1', '96.s1.a1', '96.s1.c1', '96.u1.a1', '96.u1.b1', '96.y1.b1', '96.y1.d1', '96.ba1.b1', '96.ba1.d1', '96.bf1.a1', '96.bg1.b1', '96.bj1.a1', '96.bl1.b1', '96.br1.b1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5570, -1, 5691, -1, 6098, -1, 4264, -1], 'generators': [1779365211990169, 795533260057254], 'label': '768.1090131.192.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.m1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521782
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.p1.a1', '96.x1.a1', '96.bd1.a1', '96.bk1.a1', '96.bm1.a1', '96.bu1.a1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4553, -1, 8407, -1, 4650, -1, 2614, -1], 'generators': [3846884234706384, 359890668365808], 'label': '768.1090131.192.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '192.n1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521783
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.p1.a1', '96.r1.a1', '96.r1.b1', '96.bk1.a1', '96.bn1.a1', '96.bv1.a1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [5063, -1, 8519, -1, 4924, -1, 2566, -1], 'generators': [3846541581724591, 795533260057254], 'label': '768.1090131.192.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '192.o1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521784
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.j1.a1', '96.t1.a1'], 'contains': ['384.d1.a1', '384.f1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2069, -1, 1636, -1, 2269, -1, 7738, -1], 'generators': [4253081604151, 4047630492624], 'label': '768.1090131.192.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.a1', 'old_label': '192.p1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521785
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.b1', '96.j1.b1', '96.t1.b1'], 'contains': ['384.d1.b1', '384.f1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [2069, -1, 1940, -1, 2269, -1, 7288, -1], 'generators': [1183459680839575, 4047630492624], 'label': '768.1090131.192.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.d1.b1', 'old_label': '192.p1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521786
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.l1.a1', '96.l1.a2', '96.l2.a1', '96.v1.a1', '96.v2.a1'], 'contains': ['384.d1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1500, -1, 1496, -1, 1820, -1, 8230, -1], 'generators': [359728823398327, 461960891286], 'label': '768.1090131.192.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '192.q1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521787
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.b1', '96.l1.b1', '96.l1.b2', '96.l2.b1', '96.v1.b1', '96.v2.b1'], 'contains': ['384.d1.b1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1500, -1, 3044, -1, 1820, -1, 6698, -1], 'generators': [2587548203909305, 3846242716609368], 'label': '768.1090131.192.q1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '192.q1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521788
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1024.diw', 'aut_weyl_index': 6, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1', '6.f1.a1', '6.f1.b1', '6.f1.c1', '6.f1.d1', '6.g1.a1', '6.g1.b1', '6.h1.a1', '6.h1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6627, -1, 5728, -1, 5746, -1, 4033, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 4047630492624, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521789
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.v1.a1', '24.x1.a1', '24.ba1.a1', '24.bn1.c1', '24.bn1.d1', '24.bv1.c1', '24.bv1.d1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [3333, -1, 5079, -1, 5002, -1, 5328, -1], 'generators': [1822337812123926, 4253081604151, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.l1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521790
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.a1', '96.l1.a1', '96.l2.a1', '96.v1.a1', '96.v2.a1', '96.bw1.a1', '96.bw1.b1'], 'contains': ['384.d1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1389, -1, 1466, -1, 1730, -1, 8294, -1], 'generators': [461960891286, 1822038947023849], 'label': '768.1090131.192.q2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.q2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521791
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.a2', '96.l1.a2', '96.l2.a1', '96.v1.a1', '96.v2.a1', '96.bw1.a2', '96.bw1.b2'], 'contains': ['384.d1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1389, -1, 1287, -1, 1730, -1, 8339, -1], 'generators': [312321447415, 461960891286], 'label': '768.1090131.192.q2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.q2.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521792
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.b1', '96.l1.b2', '96.l2.b1', '96.v1.b1', '96.v2.b1', '96.bw1.c1', '96.bw1.d1'], 'contains': ['384.d1.b1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1389, -1, 2925, -1, 1730, -1, 6788, -1], 'generators': [4466613169859767, 3846242716609368], 'label': '768.1090131.192.q2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.q2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521793
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.q2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.b2', '96.l1.b1', '96.l2.b1', '96.v1.b1', '96.v2.b1', '96.bw1.c2', '96.bw1.d2'], 'contains': ['384.d1.b1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1389, -1, 2955, -1, 1730, -1, 6833, -1], 'generators': [3846242716609368, 1558054095215089], 'label': '768.1090131.192.q2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.q2.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.q2.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521794
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.j1.a1', '96.z1.a1', '96.bw1.a1', '96.bw1.a2', '96.bx1.a1', '96.bx1.a2'], 'contains': ['384.e1.a1', '384.f1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1629, -1, 1078, -1, 2000, -1, 8515, -1], 'generators': [312321447414, 4047630492624], 'label': '768.1090131.192.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '192.r1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521795
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.a1', '96.j1.a1', '96.z1.b1', '96.bw1.b1', '96.bw1.b2', '96.bx1.b1', '96.bx1.b2'], 'contains': ['384.e1.a1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1629, -1, 1121, -1, 2000, -1, 8560, -1], 'generators': [735925055088, 85621839894847], 'label': '768.1090131.192.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '192.r1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521796
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.b1', '96.j1.b1', '96.z1.c1', '96.bw1.c1', '96.bw1.c2', '96.bx1.c1', '96.bx1.c2'], 'contains': ['384.e1.b1', '384.f1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1629, -1, 2068, -1, 2000, -1, 7243, -1], 'generators': [4047630492624, 1179562541714328], 'label': '768.1090131.192.r1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '192.r1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521797
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.r1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.g1.b1', '96.j1.b1', '96.z1.d1', '96.bw1.d1', '96.bw1.d2', '96.bx1.d1', '96.bx1.d2'], 'contains': ['384.e1.b1', '384.f1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1629, -1, 2098, -1, 2000, -1, 7333, -1], 'generators': [1558054095215088, 85621839894847], 'label': '768.1090131.192.r1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '192.r1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.r1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521798
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.k1.a1', '96.bb1.a1', '96.bw1.a1', '96.bw1.a2', '96.bx1.b1', '96.bx1.b2'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1032, -1, 871, -1, 1462, -1, 8766, -1], 'generators': [85895741411455, 735925055088], 'label': '768.1090131.192.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '192.s1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521799
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.k1.a1', '96.bb1.b1', '96.bw1.b1', '96.bw1.b2', '96.bx1.a1', '96.bx1.a2'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1032, -1, 1018, -1, 1462, -1, 8693, -1], 'generators': [312321447414, 4415227175928], 'label': '768.1090131.192.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '192.s1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521800
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1'], 'contains': ['24.v1.b1', '24.x1.b1', '24.ba1.b1', '24.bn1.a1', '24.bn1.b1', '24.bv1.a1', '24.bv1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3333, -1, 3142, -1, 5002, -1, 6607, -1], 'generators': [1822337812123926, 312321447414, 1183459680839575, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.l1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521801
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.b1', '96.k1.b1', '96.bb1.c1', '96.bw1.c1', '96.bw1.c2', '96.bx1.d1', '96.bx1.d2'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1032, -1, 2572, -1, 1462, -1, 6965, -1], 'generators': [3824964916138807, 1558054095215088], 'label': '768.1090131.192.s1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '192.s1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521802
{'ambient': '768.1090131', 'aut_centralizer_order': 32, 'aut_label': '192.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.b1', '96.k1.b1', '96.bb1.d1', '96.bw1.d1', '96.bw1.d2', '96.bx1.c1', '96.bx1.c2'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1032, -1, 2691, -1, 1462, -1, 7050, -1], 'generators': [3844916347312824, 1179562541714328], 'label': '768.1090131.192.s1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '192.s1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.s1.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521805
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.a1', '96.i2.a1', '96.l1.a2', '96.be1.a1', '96.bx1.a1', '96.bx1.b1'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, -1, 658, -1, 1205, -1, 8858, -1], 'generators': [312321447414, 360320459007774], 'label': '768.1090131.192.t2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '192.t2.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521806
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.a2', '96.i2.a2', '96.l1.a1', '96.be1.a1', '96.bx1.a2', '96.bx1.b2'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, -1, 737, -1, 1205, -1, 9019, -1], 'generators': [312321447414, 461960891286], 'label': '768.1090131.192.t2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '192.t2.a2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t2.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521807
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.b1', '96.i2.b1', '96.l1.b1', '96.be1.b1', '96.bx1.c1', '96.bx1.d1'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, -1, 2134, -1, 1205, -1, 7092, -1], 'generators': [1558054095215088, 5621224034334630], 'label': '768.1090131.192.t2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '192.t2.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t2.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521808
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '192.t2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.b2', '96.i2.b2', '96.l1.b2', '96.be1.b1', '96.bx1.c2', '96.bx1.d2'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, -1, 2440, -1, 1205, -1, 7378, -1], 'generators': [1558054095215088, 3846242716609368], 'label': '768.1090131.192.t2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '192.t2.b2', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.t2.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68521809
{'ambient': '768.1090131', 'aut_centralizer_order': 48, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.c1.a1', '64.c1.b1', '64.c2.a1', '64.c2.a2', '64.c2.b1', '64.c2.b2', '128.a1.a1', '128.b1.a1', '128.b1.b1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [295, -1, 386, -1, 666, -1, 9252, -1], 'generators': [84307934393430], 'label': '768.1090131.256.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68521810
{'ambient': '768.1090131', 'aut_centralizer_order': 6144, 'aut_label': '384.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.b1.a1', '192.c1.a1', '192.c1.b1', '192.d1.a1'], 'contains': ['768.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1338, 5966, 1559, 6700, 1910, 7796, 7802, 6933], 'generators': [1], 'label': '768.1090131.384.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['768.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '1.1', 'quotient_action_kernel': '384.18135', 'quotient_action_kernel_order': 384, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521811
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.f1.a1', '6.g1.a1'], 'contains': ['24.bb1.a1', '24.bd1.a1', '24.bn1.a1', '24.bo1.a1', '24.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5693, -1, 4651, -1, 5608, -1, 5518, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521812
{'ambient': '768.1090131', 'aut_centralizer_order': 2048, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.e1.a1', '192.e1.b1', '192.e2.a1', '192.e2.b1', '192.f1.a1', '192.g1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2331, -1, 2867, -1, 2393, -1, 7178, -1], 'generators': [1822337812123927], 'label': '768.1090131.384.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '384.b1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521813
{'ambient': '768.1090131', 'aut_centralizer_order': 2048, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.g1.a1', '192.h1.a1', '192.h1.b1', '192.h2.a1', '192.h2.b1', '192.i1.a1', '192.i1.b1', '192.i2.a1', '192.i2.b1', '192.j1.a1', '192.j1.b1', '192.k1.a1', '192.l1.a1', '192.m1.a1', '192.m1.b1', '192.n1.a1', '192.o1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4291, -1, 5201, -1, 4692, -1, 4500, -1], 'generators': [1822337812123926], 'label': '768.1090131.384.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '384.c1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521814
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '192.e1.a1', '192.e2.a1', '192.h1.a1', '192.h2.a1', '192.p1.a1', '192.q1.a1', '192.q2.a1', '192.q2.a2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1842, -1, 1628, -1, 2090, -1, 7750, -1], 'generators': [461960891287], 'label': '768.1090131.384.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '384.d1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521815
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.b1', '192.e1.b1', '192.e2.b1', '192.h1.b1', '192.h2.b1', '192.p1.b1', '192.q1.b1', '192.q2.b1', '192.q2.b2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1842, -1, 3016, -1, 2090, -1, 6766, -1], 'generators': [3846242716609369], 'label': '768.1090131.384.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '384.d1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521816
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '192.e1.a1', '192.e2.a1', '192.i1.a1', '192.i2.a1', '192.q1.a1', '192.q2.a1', '192.q2.a2', '192.r1.a1', '192.r1.b1', '192.s1.a1', '192.s1.b1', '192.t1.a1', '192.t2.a1', '192.t2.a2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1565, -1, 1100, -1, 1994, -1, 8361, -1], 'generators': [461960891286], 'label': '768.1090131.384.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '384.e1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521817
{'ambient': '768.1090131', 'aut_centralizer_order': 256, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.b1', '192.e1.b1', '192.e2.b1', '192.i1.b1', '192.i2.b1', '192.q1.b1', '192.q2.b1', '192.q2.b2', '192.r1.c1', '192.r1.d1', '192.s1.c1', '192.s1.d1', '192.t1.b1', '192.t2.b1', '192.t2.b2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1565, -1, 2736, -1, 1994, -1, 6900, -1], 'generators': [3846242716609368], 'label': '768.1090131.384.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '384.e1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521818
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '384.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.a1', '192.d1.a1', '192.f1.a1', '192.j1.a1', '192.p1.a1', '192.p1.b1', '192.r1.a1', '192.r1.c1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1903, -1, 1724, -1, 2169, -1, 7602, -1], 'generators': [4047630492624], 'label': '768.1090131.384.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '384.f1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.f1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521819
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '384.f1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['128.b1.b1', '192.d1.a1', '192.f1.a1', '192.j1.b1', '192.p1.a1', '192.p1.b1', '192.r1.b1', '192.r1.d1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1903, -1, 1751, -1, 2169, -1, 7641, -1], 'generators': [85621839894847], 'label': '768.1090131.384.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '384.f1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.f1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521820
{'ambient': '768.1090131', 'aut_centralizer_order': None, 'aut_label': '768.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['256.a1.a1', '384.a1.a1', '384.b1.a1', '384.c1.a1', '384.d1.a1', '384.d1.b1', '384.e1.a1', '384.e1.b1', '384.f1.a1', '384.f1.b1'], 'contains': [], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1842, 5236, 1738, 6161, 2090, 6858, 7622, 6204], 'generators': [], 'label': '768.1090131.768.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '768.a1.a1', 'normal_contained_in': ['192.a1.a1', '384.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '768.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68521821
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.f1.b1', '6.g1.b1'], 'contains': ['24.bb1.b1', '24.bd1.a1', '24.bn1.b1', '24.bo1.b1', '24.bs1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5693, -1, 4714, -1, 5608, -1, 5423, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 359890668365808, 4415227175928, 1179562541714328], 'label': '768.1090131.12.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521822
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.c1', '6.g1.a1'], 'contains': ['24.bb1.c1', '24.bd1.b1', '24.bn1.c1', '24.bo1.a1', '24.bs1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5693, -1, 5375, -1, 5608, -1, 4835, -1], 'generators': [1822337812123926, 1562082513025345, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.12.m1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521823
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.d1', '6.g1.b1'], 'contains': ['24.bb1.d1', '24.bd1.b1', '24.bn1.d1', '24.bo1.b1', '24.bs1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5693, -1, 5312, -1, 5608, -1, 4487, -1], 'generators': [1822337812123926, 1562082513025344, 4047630492625, 312321447414, 359890668365808, 1179562541714328], 'label': '768.1090131.12.m1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.m1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521824
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.f1.b1', '6.g1.a1'], 'contains': ['24.bd1.a1', '24.bs1.c1', '24.bt1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6980, -1, 5914, -1, 6162, -1, 3968, -1], 'generators': [1822337812123926, 1562082513025345, 312321447414, 1562469074861448, 359890668365808, 1179562541714328], 'label': '768.1090131.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521825
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.f1.a1', '6.g1.b1'], 'contains': ['24.bd1.a1', '24.bs1.d1', '24.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6980, -1, 5971, -1, 6162, -1, 3447, -1], 'generators': [1822337812123926, 1562082513025344, 312321447414, 359890668365808, 1179562541714328, 1562469074861449], 'label': '768.1090131.12.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521826
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.d1', '6.g1.a1'], 'contains': ['24.bd1.b1', '24.bs1.a1', '24.bt1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6980, -1, 6118, -1, 6162, -1, 2966, -1], 'generators': [4415227175929, 1822337812123926, 312321447414, 1562469074861448, 359890668365808, 1179562541714328], 'label': '768.1090131.12.n1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521827
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.c1', '6.g1.b1'], 'contains': ['24.bd1.b1', '24.bs1.b1', '24.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6980, -1, 6327, -1, 6162, -1, 2882, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 4415227175928, 1179562541714328, 1562469074861449], 'label': '768.1090131.12.n1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521828
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['192.d1.a1', '192.f1.a1', '192.p1.a1', '192.p1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['12.a1.a1', '16.c1.a1', '16.c1.b1', '16.d1.a1', '16.e1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1388, 2441, 3620, 3052, 1257, 2802, 6278, 2756], 'generators': [84307934393430, 1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '768.1090131', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68521829
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.a1', '6.f1.b1'], 'contains': ['24.w1.a1', '24.y1.a1', '24.z1.a1', '24.ba1.a1', '24.bc1.a1', '24.bd1.a1', '24.bp1.a1', '24.bq1.a1', '24.bw1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [5397, -1, 6655, -1, 4793, -1, 2671, -1], 'generators': [1822337812123926, 312321447415, 359890668365808, 461960891286, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521830
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.f1.c1', '6.f1.d1'], 'contains': ['24.w1.b1', '24.y1.b1', '24.z1.b1', '24.ba1.b1', '24.bc1.b1', '24.bd1.b1', '24.bp1.a1', '24.bq1.a1', '24.bw1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5397, -1, 6580, -1, 4793, -1, 2784, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 3846242716609368, 1558054095215089], 'label': '768.1090131.12.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.o1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521831
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.be1.a1', '24.bg1.a1', '24.bi1.a1', '24.bx1.a1', '24.bx1.b1', '24.by1.a1', '24.by1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8379, -1, 8873, -1, 8098, -1, 1013, -1], 'generators': [1558496692068486, 1822337812123926, 4253081604151, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.p1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 68521832
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.be1.a1', '24.bi1.a1', '24.bj1.a1', '24.bz1.a1', '24.bz1.b1', '24.ca1.a1', '24.ca1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8510, -1, 9142, -1, 8201, -1, 962, -1], 'generators': [1822337812123926, 4253081604151, 3846697444535406, 4047630492624, 359890668365808, 1179668884439070], 'label': '768.1090131.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.q1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 68521833
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.v1.a1', '24.x1.a1', '24.bb1.c1', '24.bb1.d1', '24.bk1.a1', '24.bm1.c1', '24.bm1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2782, -1, 5016, -1, 4154, -1, 5232, -1], 'generators': [1822337812123926, 4253081604151, 4047630492624, 1558428122581230, 359890668365808, 1179562541714328], 'label': '768.1090131.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.r1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 68521834
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1'], 'contains': ['24.v1.b1', '24.x1.b1', '24.bb1.a1', '24.bb1.b1', '24.bk1.b1', '24.bm1.a1', '24.bm1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2782, -1, 3207, -1, 4154, -1, 6511, -1], 'generators': [4415227175929, 1822337812123926, 1179762397854126, 312321447414, 4047630492624, 359890668365808], 'label': '768.1090131.12.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.r1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68521835
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.s1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.w1.a1', '24.w1.b1', '24.y1.a1', '24.y1.b1', '24.bc1.a1', '24.bc1.b1', '24.bf1.a1', '24.bg1.a1', '24.bh1.a1', '24.bk1.a1', '24.bk1.b1', '24.bl1.a1', '24.bl1.b1', '24.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4905, -1, 7188, -1, 3673, -1, 2492, -1], 'generators': [1558496692068486, 1822337812123926, 461960891287, 312321447414, 359890668365808, 3846242716609368], 'label': '768.1090131.12.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.s1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
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id: 68521836
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '12.t1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.g1.a1', '6.g1.b1'], 'contains': ['24.z1.a1', '24.z1.b1', '24.bd1.a1', '24.bd1.b1', '24.bh1.a1', '24.bj1.a1', '24.bl1.a1', '24.bl1.b1', '24.bu1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5856, -1, 7264, -1, 5400, -1, 2259, -1], 'generators': [1822337812123926, 1558428122581230, 359890668365808, 461960891286, 3846242716609368, 1558054095215089], 'label': '768.1090131.12.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.t1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.t1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
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id: 68521837
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.a1', '6.f1.c1'], 'contains': ['24.bo1.a1', '24.bq1.a1', '24.bt1.a1', '24.bx1.a1', '24.bz1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8241, -1, 7435, -1, 7540, -1, 1738, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 1179562541714328, 1562469074861449], 'label': '768.1090131.12.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
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id: 68521838
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.u1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.f1.b1', '6.f1.d1'], 'contains': ['24.bo1.b1', '24.bq1.a1', '24.bt1.b1', '24.bx1.b1', '24.bz1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8241, -1, 7401, -1, 7540, -1, 1840, -1], 'generators': [1822337812123926, 4047630492625, 312321447414, 1562469074861448, 359890668365808, 1179562541714328], 'label': '768.1090131.12.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.u1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.u1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521839
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '8.d1.a1', '8.d1.b1', '12.h1.a1', '16.a1.a1', '16.b1.a1', '16.b1.a2'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [803, -1, 410, -1, 885, -1, 9053, -1], 'generators': [84307934393430, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286, 85621839894847], 'label': '768.1090131.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521840
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.a1', '6.h1.a1'], 'contains': ['24.bo1.a1', '24.bt1.b1', '24.bu1.a1', '24.by1.a1', '24.ca1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7652, -1, 8112, -1, 7309, -1, 2027, -1], 'generators': [1558496692068486, 1822337812123926, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.12.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521841
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.v1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.g1.b1', '6.h1.b1'], 'contains': ['24.bo1.b1', '24.bt1.a1', '24.bu1.a1', '24.by1.b1', '24.ca1.b1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7652, -1, 8146, -1, 7309, -1, 1789, -1], 'generators': [1822337812123926, 3846541581724590, 3846697444535406, 359890668365808, 1558054095215088, 85621839894847], 'label': '768.1090131.12.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.v1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.v1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521842
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.a1', '6.f1.d1'], 'contains': ['24.bq1.a1', '24.bs1.a1', '24.bs1.d1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7230, -1, 5137, -1, 6483, -1, 4320, -1], 'generators': [4415227175929, 1822337812123926, 1562082513025344, 312321447414, 359890668365808, 1179562541714328], 'label': '768.1090131.12.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521843
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.w1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.f1.b1', '6.f1.c1'], 'contains': ['24.bq1.a1', '24.bs1.b1', '24.bs1.c1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7230, -1, 4894, -1, 6483, -1, 4574, -1], 'generators': [1822337812123926, 1562082513025345, 312321447414, 359890668365808, 4415227175928, 1179562541714328], 'label': '768.1090131.12.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.w1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.w1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
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id: 68521844
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.a1', '6.h1.b1'], 'contains': ['24.bs1.a1', '24.bs1.c1', '24.bu1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7106, -1, 4841, -1, 6325, -1, 4653, -1], 'generators': [1822337812123926, 3846541581724590, 3846697444535406, 85895741411455, 359890668365808, 1558054095215088], 'label': '768.1090131.12.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521845
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.x1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.g1.b1', '6.h1.a1'], 'contains': ['24.bs1.b1', '24.bs1.d1', '24.bu1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7106, -1, 5190, -1, 6325, -1, 4399, -1], 'generators': [1558496692068486, 1822337812123926, 312321447414, 359890668365808, 4415227175928, 1179562541714328], 'label': '768.1090131.12.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.x1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.x1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521846
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.a1', '6.h1.a1'], 'contains': ['24.bm1.c1', '24.bo1.a1', '24.bs1.d1', '24.bv1.c1', '24.bw1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4387, -1, 5248, -1, 5192, -1, 4740, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521847
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1', '6.f1.b1', '6.h1.b1'], 'contains': ['24.bm1.d1', '24.bo1.b1', '24.bs1.c1', '24.bv1.d1', '24.bw1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4387, -1, 4952, -1, 5192, -1, 4931, -1], 'generators': [1822337812123926, 359890668365808, 1558054095215088, 735925055088, 3846242716609368, 85621839894847], 'label': '768.1090131.12.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521848
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.f1.c1', '6.h1.a1'], 'contains': ['24.bm1.a1', '24.bo1.a1', '24.bs1.b1', '24.bv1.a1', '24.bw1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4387, -1, 4587, -1, 5192, -1, 5614, -1], 'generators': [1822337812123926, 312321447414, 4047630492624, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.12.y1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521849
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1', '6.f1.d1', '6.h1.b1'], 'contains': ['24.bm1.b1', '24.bo1.b1', '24.bs1.a1', '24.bv1.b1', '24.bw1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4387, -1, 4523, -1, 5192, -1, 5709, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 85621839894847], 'label': '768.1090131.12.y1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.y1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.y1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521850
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.b1', '8.d1.c1', '8.d1.d1', '12.h1.b1', '16.a1.a1', '16.b1.b1', '16.b1.b2'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [803, -1, 811, -1, 885, -1, 8132, -1], 'generators': [84307934393430, 1822337812123926, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.4.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '4.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521851
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.a1', '6.h1.b1'], 'contains': ['24.bs1.a1', '24.bt1.a1', '24.bw1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6816, -1, 5802, -1, 5994, -1, 3614, -1], 'generators': [1822337812123926, 85895741411455, 359890668365808, 1558054095215088, 735925055088, 3846242716609368], 'label': '768.1090131.12.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521852
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1', '6.f1.b1', '6.h1.a1'], 'contains': ['24.bs1.b1', '24.bt1.b1', '24.bw1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6816, -1, 5859, -1, 5994, -1, 3530, -1], 'generators': [1822337812123926, 312321447414, 359890668365808, 4415227175928, 1558054095215088, 3846242716609368], 'label': '768.1090131.12.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521853
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.f1.c1', '6.h1.b1'], 'contains': ['24.bs1.c1', '24.bt1.a1', '24.bw1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6816, -1, 5691, -1, 5994, -1, 4136, -1], 'generators': [1822337812123926, 3824964916138807, 312321447414, 359890668365808, 461960891286, 1558054095215088], 'label': '768.1090131.12.z1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.c1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.c1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521854
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '12.z1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1', '6.f1.d1', '6.h1.a1'], 'contains': ['24.bs1.d1', '24.bt1.b1', '24.bw1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6816, -1, 5747, -1, 5994, -1, 4052, -1], 'generators': [1822337812123926, 1562082513025344, 312321447414, 359890668365808, 461960891286, 1179562541714328], 'label': '768.1090131.12.z1.d1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.z1.d1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.z1.d1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68521855
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.b1.b1', '4.c1.a1'], 'contains': ['32.a1.a1', '32.c1.a1', '32.c1.b1', '48.p1.a1', '64.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [875, -1, 2531, -1, 938, -1, 7808, -1], 'generators': [84307934393430, 1822337812123926, 4047630492624, 359890668365808, 85621839894847], 'label': '768.1090131.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521856
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['32.b2.a1', '32.d1.a1', '32.d1.b1', '48.s1.a1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [298, -1, 138, -1, 391, -1, 9496, -1], 'generators': [84307934393430, 4047630492624, 359728823398326, 85621839894847, 1821883084207920], 'label': '768.1090131.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521857
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['32.b2.a2', '32.d1.a2', '32.d1.b2', '48.s1.a2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [298, -1, 244, -1, 391, -1, 9591, -1], 'generators': [84307934393430, 312321447414, 4047630492624, 461960891286, 85621839894847], 'label': '768.1090131.16.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '16.b1.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521858
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['32.b2.b1', '32.d1.c1', '32.d1.d1', '48.s1.b1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [298, -1, 466, -1, 391, -1, 8888, -1], 'generators': [84307934393430, 4047630492624, 3437629559701230, 85621839894847, 4934975208295326], 'label': '768.1090131.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521859
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['32.b2.b2', '32.d1.c2', '32.d1.d2', '48.s1.b2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [298, -1, 579, -1, 391, -1, 9053, -1], 'generators': [84307934393430, 4047630492624, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.16.b1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '16.b1.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521860
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1', '8.d1.a1', '8.d1.b1'], 'contains': ['48.a1.a1', '64.b1.a1', '64.c1.a1', '64.c2.a1', '64.c2.a2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [573, -1, 318, -1, 526, -1, 9701, -1], 'generators': [84307934393430, 1822337812123926, 312321447414, 359890668365808, 461960891286], 'label': '768.1090131.16.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.c1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521861
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.e1.b1', '12.k1.a1', '16.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1700, -1, 6230, -1, 1538, -1, 3299, -1], 'generators': [84307934393430, 1822337812123926, 3846697444535406, 4047630492624, 359890668365808, 1179668884439070, 85621839894847], 'label': '768.1090131.4.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '4.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68521862
{'ambient': '768.1090131', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.b1', '8.d1.c1', '8.d1.d1'], 'contains': ['48.a1.b1', '64.b1.a1', '64.c1.b1', '64.c2.b1', '64.c2.b2'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [573, -1, 985, -1, 526, -1, 8317, -1], 'generators': [84307934393430, 1822337812123926, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.16.c1.b1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '16.c1.b1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68521863
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.b1.a1', '8.e1.a1', '8.e1.b1'], 'contains': ['48.b1.a1', '64.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1634, -1, 6263, -1, 1258, -1, 3410, -1], 'generators': [84307934393430, 1822337812123926, 3846697444535406, 359890668365808, 1179668884439070], 'label': '768.1090131.16.d1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.d1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68521864
{'ambient': '768.1090131', 'aut_centralizer_order': 2, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.c1.a1'], 'contains': ['48.cp1.a1', '64.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1237, -1, 5559, -1, 1112, -1, 6245, -1], 'generators': [84307934393430, 1558496692068486, 1822337812123926, 3846541581724590, 359890668365808], 'label': '768.1090131.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.e1.a1', 'projective_image': '768.1090131', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
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id: 68521865
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': ['32.d1.c2', '32.d1.d2', '32.d1.d1', '32.d1.c1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.h1.a1', '12.i1.b1'], 'contains': ['48.a1.a1', '48.i1.a1', '48.o1.a1', '48.y1.a1', '48.bw1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1858, 4608, 2198, 9098, 1977, 9250, 7558, 6631], 'generators': [1822337812123926, 312321447414, 359890668365808, 1, 461960891286], 'label': '768.1090131.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 68521866
{'ambient': '768.1090131', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.b1', 'complements': ['32.d1.a2', '32.d1.b2', '32.d1.b1', '32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.h1.b1', '12.i1.a1'], 'contains': ['48.a1.b1', '48.i1.b1', '48.o1.b1', '48.y1.b1', '48.bw1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1858, 4608, 3845, 7524, 1977, 9250, 5706, 5173], 'generators': [1822337812123926, 359890668365808, 1, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.b1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
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id: 68521867
{'ambient': '768.1090131', 'aut_centralizer_order': 128, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['32.d1.c2', '32.d1.c1', '32.d1.d2', '32.d1.d1', '32.d1.b2', '32.d1.b1', '32.d1.a2', '32.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.g1.a1', '12.k1.a1'], 'contains': ['48.b1.a1', '48.q1.a1', '48.ck1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7813, 7742, 8876, 4491, 7400, 6436, 1286, 8764], 'generators': [1822337812123926, 3846697444535406, 359890668365808, 1, 1179668884439070], 'label': '768.1090131.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.b1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68521868
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['48.c1.a1', '48.c1.b1', '48.e1.a1', '48.e1.b1', '48.g1.a1', '48.j1.a1', '48.l1.a1', '48.bc1.a1', '48.bc1.b1', '48.bc1.c1', '48.bc1.d1', '48.bg1.a1', '48.bg1.b1', '48.bi1.a1', '48.bi1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6513, -1, 5506, -1, 6818, -1, 4302, -1], 'generators': [312321447414, 1821036378652951, 359890668365808, 1179562541714328, 1821036378652950], 'label': '768.1090131.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521869
{'ambient': '768.1090131', 'aut_centralizer_order': 16, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1'], 'contains': ['48.c1.a1', '48.c1.b1', '48.d1.a1', '48.d1.b1', '48.g1.a1', '48.j1.a1', '48.k1.a1', '48.bd1.a1', '48.bd1.b1', '48.bd1.c1', '48.bd1.d1', '48.bh1.a1', '48.bh1.b1', '48.bj1.a1', '48.bj1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6652, -1, 4899, -1, 6392, -1, 4701, -1], 'generators': [4047630492625, 312321447414, 4047630492624, 359890668365808, 1179562541714328], 'label': '768.1090131.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '24.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521870
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.i1.a1', '48.s1.a1', '48.s1.a2', '48.t1.a1', '48.t1.a2', '48.be1.a1', '48.be1.b1', '48.bk1.a1', '48.bk1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1132, -1, 1248, -1, 1449, -1, 8652, -1], 'generators': [4047630492625, 312321447414, 4047630492624, 359890668365808, 461960891286], 'label': '768.1090131.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68521871
{'ambient': '768.1090131', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.d1.b1', '48.f1.b1', '48.i1.b1', '48.s1.b1', '48.s1.b2', '48.t1.b1', '48.t1.b2', '48.be1.c1', '48.be1.d1', '48.bk1.c1', '48.bk1.d1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1132, -1, 2919, -1, 1449, -1, 6910, -1], 'generators': [4047630492625, 4047630492624, 359890668365808, 1558054095215088, 3846242716609368], 'label': '768.1090131.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
