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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '240.84', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [20, 10, 4, 10, 60], 'aut_gens': [[1, 120, 1320], [15811, 21360, 12240], [24811, 8040, 28680], [24811, 10920, 25920], [27251, 19200, 7080], [19921, 19200, 23280]], 'aut_group': None, 'aut_hash': 8062377920923750923, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 116160, 'aut_permdeg': 486, 'aut_perms': 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'aut_phi_ratio': 16.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 1, 4], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 1, 12], [11, 40, 3, 1], [12, 121, 4, 2], [15, 121, 2, 4], [20, 121, 2, 8], [22, 40, 3, 1], [24, 121, 8, 2], [30, 121, 2, 12], [33, 40, 6, 1], [40, 121, 4, 8], [60, 121, 4, 8], [66, 40, 6, 1], [120, 121, 8, 8]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 121, 2], [3, 1, 2], [4, 121, 4], [5, 121, 4], [6, 1, 2], [6, 121, 4], [8, 121, 8], [10, 121, 12], [11, 40, 3], [12, 121, 8], [15, 121, 8], [20, 121, 16], [22, 40, 3], [24, 121, 16], [30, 121, 24], [33, 40, 6], [40, 121, 32], [60, 121, 32], [66, 40, 6], [120, 121, 64]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '4840.c', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '11.1', '11.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4840.c', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 121, 1, 2], [3, 1, 2, 1], [4, 121, 2, 2], [5, 121, 4, 1], [6, 1, 2, 1], [6, 121, 2, 2], [8, 121, 4, 2], [10, 121, 4, 3], [11, 40, 1, 3], [12, 121, 4, 2], [15, 121, 8, 1], [20, 121, 8, 2], [22, 40, 1, 3], [24, 121, 8, 2], [30, 121, 8, 3], [33, 40, 2, 3], [40, 121, 16, 2], [60, 121, 16, 2], [66, 40, 2, 3], [120, 121, 32, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2304, 'exponent': 1320, 'exponents_of_order': [4, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[40, 0, 6]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '29040.c', 'hash': 1832492014362143934, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 440, 'inner_gen_orders': [40, 11, 11], 'inner_gens': [[1, 22200, 12840], [8281, 120, 1320], [18841, 120, 1320]], 'inner_hash': 1340125317553616686, 'inner_nilpotent': False, 'inner_order': 4840, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_{40}', 'inner_used': [1, 2], 'irrC_degree': 40, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 80, 'irrep_stats': [[1, 240], [40, 18]], 'label': '29040.c', 'linC_count': 6, 'linC_degree': 40, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 42, 'linQ_degree_count': 18, 'linQ_dim': 42, 'linQ_dim_count': 18, 'linR_count': 360, 'linR_degree': 42, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C11^2:C120', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 84, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 258, 'number_divisions': 44, 'number_normal_subgroups': 48, 'number_subgroup_autclasses': 100, 'number_subgroup_classes': 148, 'number_subgroups': 7048, 'old_label': None, 'order': 29040, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 243], [3, 2], [4, 484], [5, 484], [6, 486], [8, 968], [10, 1452], [11, 120], [12, 968], [15, 968], [20, 1936], [22, 120], [24, 1936], [30, 2904], [33, 240], [40, 3872], [60, 3872], [66, 240], [120, 7744]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 102], 'outer_gens': [[41, 1200, 27720], [91, 27000, 22560], [14521, 21480, 4920]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 49, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 8], [8, 8], [16, 4], [32, 2], [40, 6], [80, 6]], 'representations': {'PC': {'code': '172219749243564175609130683064643333843943974933224474218801318983668488034901316703038770080775900013909', 'gens': [1, 6, 7], 'pres': [8, 2, 2, 2, 3, 5, 11, 2, 11, 16, 41, 66, 123, 1065605, 63373, 2901, 2909, 2197, 719046, 409934, 240262, 138630, 27758, 166, 1559047, 7695, 84503, 84511, 63399]}, 'GLFq': {'d': 2, 'q': 121, 'gens': [16280793, 207272754, 140740226, 80979421, 1830210, 207916856, 58532609, 26573430]}, 'Perm': {'d': 49, 'gens': [14000005658767194322138849151509273456093287375561934835649870, 26667169170766690187178353532046274075554480316325393817632000, 30, 39334312563777554177172541404234401431449219459601552468275840, 52045486600559582527271472987696799888995126791267305791810481, 64672597377446824496185695107136948366849105137185555170832590, 77330186214435394099468424732940748724002691259426604052585550, 31]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 120], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{11}^2:C_{120}', 'transitive_degree': 264, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 109628294
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 3, 'group_order': 29040, 'label': '1A', 'order': 1, 'powers': [1, 1, 1, 1], 'representative': 0, 'size': 1}
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id: 109628405
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 3, 'group_order': 29040, 'label': '2A', 'order': 2, 'powers': [1, 2, 2, 2], 'representative': 14520, 'size': 1}
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id: 109628475
{'aut_label': '2B', 'centralizer': '121.a1.a1', 'counter': 3, 'group_counter': 3, 'group_order': 29040, 'label': '2B', 'order': 2, 'powers': [1, 3, 3, 3], 'representative': 11940, 'size': 121}
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id: 109628486
{'aut_label': '2C', 'centralizer': '121.a1.a1', 'counter': 4, 'group_counter': 3, 'group_order': 29040, 'label': '2C', 'order': 2, 'powers': [1, 4, 4, 4], 'representative': 27540, 'size': 121}
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id: 109628497
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 5, 'group_counter': 3, 'group_order': 29040, 'label': '3A1', 'order': 3, 'powers': [6, 1, 6, 6], 'representative': 80, 'size': 1}
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id: 109628508
{'aut_label': '3A1', 'centralizer': '1.a1.a1', 'counter': 6, 'group_counter': 3, 'group_order': 29040, 'label': '3A-1', 'order': 3, 'powers': [5, 1, 5, 5], 'representative': 40, 'size': 1}
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id: 109628519
{'aut_label': '4A1', 'centralizer': '121.a1.a1', 'counter': 7, 'group_counter': 3, 'group_order': 29040, 'label': '4A1', 'order': 4, 'powers': [4, 8, 7, 8], 'representative': 17910, 'size': 121}
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id: 109628530
{'aut_label': '4A1', 'centralizer': '121.a1.a1', 'counter': 8, 'group_counter': 3, 'group_order': 29040, 'label': '4A-1', 'order': 4, 'powers': [4, 7, 8, 7], 'representative': 9690, 'size': 121}
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id: 109628541
{'aut_label': '4B1', 'centralizer': '121.a1.a1', 'counter': 9, 'group_counter': 3, 'group_order': 29040, 'label': '4B1', 'order': 4, 'powers': [4, 10, 9, 10], 'representative': 30, 'size': 121}
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id: 109628295
{'aut_label': '4B1', 'centralizer': '121.a1.a1', 'counter': 10, 'group_counter': 3, 'group_order': 29040, 'label': '4B-1', 'order': 4, 'powers': [4, 9, 10, 9], 'representative': 90, 'size': 121}
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id: 109628306
{'aut_label': '5A1', 'centralizer': '121.a1.a1', 'counter': 11, 'group_counter': 3, 'group_order': 29040, 'label': '5A1', 'order': 5, 'powers': [13, 14, 1, 11], 'representative': 15888, 'size': 121}
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id: 109628317
{'aut_label': '5A-1', 'centralizer': '121.a1.a1', 'counter': 12, 'group_counter': 3, 'group_order': 29040, 'label': '5A-1', 'order': 5, 'powers': [14, 13, 1, 12], 'representative': 10632, 'size': 121}
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id: 109628328
{'aut_label': '5A2', 'centralizer': '121.a1.a1', 'counter': 13, 'group_counter': 3, 'group_order': 29040, 'label': '5A2', 'order': 5, 'powers': [12, 11, 1, 13], 'representative': 21216, 'size': 121}
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id: 109628339
{'aut_label': '5A-2', 'centralizer': '121.a1.a1', 'counter': 14, 'group_counter': 3, 'group_order': 29040, 'label': '5A-2', 'order': 5, 'powers': [11, 12, 1, 14], 'representative': 13224, 'size': 121}
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id: 109628350
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 15, 'group_counter': 3, 'group_order': 29040, 'label': '6A1', 'order': 6, 'powers': [5, 2, 16, 16], 'representative': 14560, 'size': 1}
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id: 109628361
{'aut_label': '6A1', 'centralizer': '1.a1.a1', 'counter': 16, 'group_counter': 3, 'group_order': 29040, 'label': '6A-1', 'order': 6, 'powers': [6, 2, 15, 15], 'representative': 14600, 'size': 1}
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id: 109628372
{'aut_label': '6B1', 'centralizer': '121.a1.a1', 'counter': 17, 'group_counter': 3, 'group_order': 29040, 'label': '6B1', 'order': 6, 'powers': [6, 3, 18, 18], 'representative': 11900, 'size': 121}
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id: 109628383
{'aut_label': '6B1', 'centralizer': '121.a1.a1', 'counter': 18, 'group_counter': 3, 'group_order': 29040, 'label': '6B-1', 'order': 6, 'powers': [5, 3, 17, 17], 'representative': 11980, 'size': 121}
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id: 109628394
{'aut_label': '6C1', 'centralizer': '121.a1.a1', 'counter': 19, 'group_counter': 3, 'group_order': 29040, 'label': '6C1', 'order': 6, 'powers': [6, 4, 20, 20], 'representative': 27500, 'size': 121}
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id: 109628406
{'aut_label': '6C1', 'centralizer': '121.a1.a1', 'counter': 20, 'group_counter': 3, 'group_order': 29040, 'label': '6C-1', 'order': 6, 'powers': [5, 4, 19, 19], 'representative': 27580, 'size': 121}
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id: 109628417
{'aut_label': '8A1', 'centralizer': '121.a1.a1', 'counter': 21, 'group_counter': 3, 'group_order': 29040, 'label': '8A1', 'order': 8, 'powers': [9, 23, 24, 23], 'representative': 15, 'size': 121}
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id: 109628428
{'aut_label': '8A-1', 'centralizer': '121.a1.a1', 'counter': 22, 'group_counter': 3, 'group_order': 29040, 'label': '8A-1', 'order': 8, 'powers': [10, 24, 23, 24], 'representative': 105, 'size': 121}
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id: 109628439
{'aut_label': '8A1', 'centralizer': '121.a1.a1', 'counter': 23, 'group_counter': 3, 'group_order': 29040, 'label': '8A3', 'order': 8, 'powers': [10, 21, 22, 21], 'representative': 45, 'size': 121}
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id: 109628450
{'aut_label': '8A-1', 'centralizer': '121.a1.a1', 'counter': 24, 'group_counter': 3, 'group_order': 29040, 'label': '8A-3', 'order': 8, 'powers': [9, 22, 21, 22], 'representative': 75, 'size': 121}
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id: 109628461
{'aut_label': '8A1', 'centralizer': '121.a1.a1', 'counter': 25, 'group_counter': 3, 'group_order': 29040, 'label': '8B1', 'order': 8, 'powers': [9, 27, 28, 27], 'representative': 11895, 'size': 121}
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id: 109628471
{'aut_label': '8A-1', 'centralizer': '121.a1.a1', 'counter': 26, 'group_counter': 3, 'group_order': 29040, 'label': '8B-1', 'order': 8, 'powers': [10, 28, 27, 28], 'representative': 25305, 'size': 121}
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id: 109628472
{'aut_label': '8A1', 'centralizer': '121.a1.a1', 'counter': 27, 'group_counter': 3, 'group_order': 29040, 'label': '8B3', 'order': 8, 'powers': [10, 25, 26, 25], 'representative': 23325, 'size': 121}
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id: 109628473
{'aut_label': '8A-1', 'centralizer': '121.a1.a1', 'counter': 28, 'group_counter': 3, 'group_order': 29040, 'label': '8B-3', 'order': 8, 'powers': [9, 26, 25, 26], 'representative': 7635, 'size': 121}
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id: 109628474
{'aut_label': '10A1', 'centralizer': '121.a1.a1', 'counter': 29, 'group_counter': 3, 'group_order': 29040, 'label': '10A1', 'order': 10, 'powers': [11, 31, 2, 29], 'representative': 27744, 'size': 121}
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id: 109628476
{'aut_label': '10A-1', 'centralizer': '121.a1.a1', 'counter': 30, 'group_counter': 3, 'group_order': 29040, 'label': '10A-1', 'order': 10, 'powers': [12, 32, 2, 30], 'representative': 6696, 'size': 121}
-
id: 109628477
{'aut_label': '10A3', 'centralizer': '121.a1.a1', 'counter': 31, 'group_counter': 3, 'group_order': 29040, 'label': '10A3', 'order': 10, 'powers': [14, 30, 2, 31], 'representative': 25152, 'size': 121}
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id: 109628478
{'aut_label': '10A-3', 'centralizer': '121.a1.a1', 'counter': 32, 'group_counter': 3, 'group_order': 29040, 'label': '10A-3', 'order': 10, 'powers': [13, 29, 2, 32], 'representative': 1368, 'size': 121}
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id: 109628479
{'aut_label': '10B1', 'centralizer': '121.a1.a1', 'counter': 33, 'group_counter': 3, 'group_order': 29040, 'label': '10B1', 'order': 10, 'powers': [14, 35, 3, 33], 'representative': 9252, 'size': 121}
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id: 109628480
{'aut_label': '10B-1', 'centralizer': '121.a1.a1', 'counter': 34, 'group_counter': 3, 'group_order': 29040, 'label': '10B-1', 'order': 10, 'powers': [13, 36, 3, 34], 'representative': 22548, 'size': 121}
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id: 109628481
{'aut_label': '10B3', 'centralizer': '121.a1.a1', 'counter': 35, 'group_counter': 3, 'group_order': 29040, 'label': '10B3', 'order': 10, 'powers': [12, 34, 3, 35], 'representative': 6636, 'size': 121}
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id: 109628482
{'aut_label': '10B-3', 'centralizer': '121.a1.a1', 'counter': 36, 'group_counter': 3, 'group_order': 29040, 'label': '10B-3', 'order': 10, 'powers': [11, 33, 3, 36], 'representative': 1404, 'size': 121}
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id: 109628483
{'aut_label': '10C1', 'centralizer': '121.a1.a1', 'counter': 37, 'group_counter': 3, 'group_order': 29040, 'label': '10C1', 'order': 10, 'powers': [14, 39, 4, 37], 'representative': 24612, 'size': 121}
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id: 109628484
{'aut_label': '10C-1', 'centralizer': '121.a1.a1', 'counter': 38, 'group_counter': 3, 'group_order': 29040, 'label': '10C-1', 'order': 10, 'powers': [13, 40, 4, 38], 'representative': 8748, 'size': 121}
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id: 109628485
{'aut_label': '10C3', 'centralizer': '121.a1.a1', 'counter': 39, 'group_counter': 3, 'group_order': 29040, 'label': '10C3', 'order': 10, 'powers': [12, 38, 4, 39], 'representative': 21756, 'size': 121}
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id: 109628487
{'aut_label': '10C-3', 'centralizer': '121.a1.a1', 'counter': 40, 'group_counter': 3, 'group_order': 29040, 'label': '10C-3', 'order': 10, 'powers': [11, 37, 4, 40], 'representative': 16044, 'size': 121}
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id: 109628488
{'aut_label': '11A', 'centralizer': '40.a1.a1', 'counter': 41, 'group_counter': 3, 'group_order': 29040, 'label': '11A', 'order': 11, 'powers': [41, 41, 41, 1], 'representative': 7920, 'size': 40}
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id: 109628489
{'aut_label': '11A', 'centralizer': '40.a1.a1', 'counter': 42, 'group_counter': 3, 'group_order': 29040, 'label': '11B', 'order': 11, 'powers': [42, 42, 42, 1], 'representative': 8640, 'size': 40}
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id: 109628490
{'aut_label': '11A', 'centralizer': '40.a1.a1', 'counter': 43, 'group_counter': 3, 'group_order': 29040, 'label': '11C', 'order': 11, 'powers': [43, 43, 43, 1], 'representative': 8880, 'size': 40}
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id: 109628491
{'aut_label': '12A1', 'centralizer': '121.a1.a1', 'counter': 44, 'group_counter': 3, 'group_order': 29040, 'label': '12A1', 'order': 12, 'powers': [19, 7, 46, 45], 'representative': 9610, 'size': 121}
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id: 109628492
{'aut_label': '12A1', 'centralizer': '121.a1.a1', 'counter': 45, 'group_counter': 3, 'group_order': 29040, 'label': '12A-1', 'order': 12, 'powers': [20, 8, 47, 44], 'representative': 17990, 'size': 121}
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id: 109628493
{'aut_label': '12A1', 'centralizer': '121.a1.a1', 'counter': 46, 'group_counter': 3, 'group_order': 29040, 'label': '12A5', 'order': 12, 'powers': [20, 7, 44, 47], 'representative': 9650, 'size': 121}
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id: 109628494
{'aut_label': '12A1', 'centralizer': '121.a1.a1', 'counter': 47, 'group_counter': 3, 'group_order': 29040, 'label': '12A-5', 'order': 12, 'powers': [19, 8, 45, 46], 'representative': 17950, 'size': 121}
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id: 109628495
{'aut_label': '12B1', 'centralizer': '121.a1.a1', 'counter': 48, 'group_counter': 3, 'group_order': 29040, 'label': '12B1', 'order': 12, 'powers': [19, 9, 50, 49], 'representative': 10, 'size': 121}
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id: 109628496
{'aut_label': '12B1', 'centralizer': '121.a1.a1', 'counter': 49, 'group_counter': 3, 'group_order': 29040, 'label': '12B-1', 'order': 12, 'powers': [20, 10, 51, 48], 'representative': 110, 'size': 121}
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id: 109628498
{'aut_label': '12B1', 'centralizer': '121.a1.a1', 'counter': 50, 'group_counter': 3, 'group_order': 29040, 'label': '12B5', 'order': 12, 'powers': [20, 9, 48, 51], 'representative': 50, 'size': 121}
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id: 109628499
{'aut_label': '12B1', 'centralizer': '121.a1.a1', 'counter': 51, 'group_counter': 3, 'group_order': 29040, 'label': '12B-5', 'order': 12, 'powers': [19, 10, 49, 50], 'representative': 70, 'size': 121}
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id: 109628500
{'aut_label': '15A1', 'centralizer': '121.a1.a1', 'counter': 52, 'group_counter': 3, 'group_order': 29040, 'label': '15A1', 'order': 15, 'powers': [54, 11, 5, 57], 'representative': 21136, 'size': 121}
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id: 109628501
{'aut_label': '15A-1', 'centralizer': '121.a1.a1', 'counter': 53, 'group_counter': 3, 'group_order': 29040, 'label': '15A-1', 'order': 15, 'powers': [55, 12, 6, 56], 'representative': 13304, 'size': 121}
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id: 109628502
{'aut_label': '15A2', 'centralizer': '121.a1.a1', 'counter': 54, 'group_counter': 3, 'group_order': 29040, 'label': '15A2', 'order': 15, 'powers': [56, 13, 6, 58], 'representative': 10592, 'size': 121}
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id: 109628503
{'aut_label': '15A-2', 'centralizer': '121.a1.a1', 'counter': 55, 'group_counter': 3, 'group_order': 29040, 'label': '15A-2', 'order': 15, 'powers': [57, 14, 5, 59], 'representative': 15928, 'size': 121}
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id: 109628504
{'aut_label': '15A-1', 'centralizer': '121.a1.a1', 'counter': 56, 'group_counter': 3, 'group_order': 29040, 'label': '15A4', 'order': 15, 'powers': [59, 12, 5, 53], 'representative': 13264, 'size': 121}
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id: 109628505
{'aut_label': '15A1', 'centralizer': '121.a1.a1', 'counter': 57, 'group_counter': 3, 'group_order': 29040, 'label': '15A-4', 'order': 15, 'powers': [58, 11, 6, 52], 'representative': 21176, 'size': 121}
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id: 109628506
{'aut_label': '15A2', 'centralizer': '121.a1.a1', 'counter': 58, 'group_counter': 3, 'group_order': 29040, 'label': '15A7', 'order': 15, 'powers': [53, 13, 5, 54], 'representative': 10672, 'size': 121}
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id: 109628507
{'aut_label': '15A-2', 'centralizer': '121.a1.a1', 'counter': 59, 'group_counter': 3, 'group_order': 29040, 'label': '15A-7', 'order': 15, 'powers': [52, 14, 6, 55], 'representative': 15848, 'size': 121}
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id: 109628509
{'aut_label': '20A1', 'centralizer': '121.a1.a1', 'counter': 60, 'group_counter': 3, 'group_order': 29040, 'label': '20A1', 'order': 20, 'powers': [37, 62, 7, 67], 'representative': 4086, 'size': 121}
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id: 109628510
{'aut_label': '20A-1', 'centralizer': '121.a1.a1', 'counter': 61, 'group_counter': 3, 'group_order': 29040, 'label': '20A-1', 'order': 20, 'powers': [38, 63, 8, 66], 'representative': 6954, 'size': 121}
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id: 109628511
{'aut_label': '20A3', 'centralizer': '121.a1.a1', 'counter': 62, 'group_counter': 3, 'group_order': 29040, 'label': '20A3', 'order': 20, 'powers': [39, 66, 8, 65], 'representative': 12378, 'size': 121}
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id: 109628512
{'aut_label': '20A-3', 'centralizer': '121.a1.a1', 'counter': 63, 'group_counter': 3, 'group_order': 29040, 'label': '20A-3', 'order': 20, 'powers': [40, 67, 7, 64], 'representative': 26262, 'size': 121}
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id: 109628513
{'aut_label': '20A-3', 'centralizer': '121.a1.a1', 'counter': 64, 'group_counter': 3, 'group_order': 29040, 'label': '20A7', 'order': 20, 'powers': [40, 60, 8, 63], 'representative': 1362, 'size': 121}
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id: 109628514
{'aut_label': '20A3', 'centralizer': '121.a1.a1', 'counter': 65, 'group_counter': 3, 'group_order': 29040, 'label': '20A-7', 'order': 20, 'powers': [39, 61, 7, 62], 'representative': 15198, 'size': 121}
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id: 109628515
{'aut_label': '20A-1', 'centralizer': '121.a1.a1', 'counter': 66, 'group_counter': 3, 'group_order': 29040, 'label': '20A9', 'order': 20, 'powers': [38, 64, 7, 61], 'representative': 20694, 'size': 121}
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id: 109628516
{'aut_label': '20A1', 'centralizer': '121.a1.a1', 'counter': 67, 'group_counter': 3, 'group_order': 29040, 'label': '20A-9', 'order': 20, 'powers': [37, 65, 8, 60], 'representative': 23466, 'size': 121}
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id: 109628517
{'aut_label': '20B1', 'centralizer': '121.a1.a1', 'counter': 68, 'group_counter': 3, 'group_order': 29040, 'label': '20B1', 'order': 20, 'powers': [37, 70, 9, 75], 'representative': 6, 'size': 121}
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id: 109628518
{'aut_label': '20B-1', 'centralizer': '121.a1.a1', 'counter': 69, 'group_counter': 3, 'group_order': 29040, 'label': '20B-1', 'order': 20, 'powers': [38, 71, 10, 74], 'representative': 114, 'size': 121}
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id: 109628520
{'aut_label': '20B3', 'centralizer': '121.a1.a1', 'counter': 70, 'group_counter': 3, 'group_order': 29040, 'label': '20B3', 'order': 20, 'powers': [39, 74, 10, 73], 'representative': 18, 'size': 121}
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id: 109628521
{'aut_label': '20B-3', 'centralizer': '121.a1.a1', 'counter': 71, 'group_counter': 3, 'group_order': 29040, 'label': '20B-3', 'order': 20, 'powers': [40, 75, 9, 72], 'representative': 102, 'size': 121}
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id: 109628522
{'aut_label': '20B-3', 'centralizer': '121.a1.a1', 'counter': 72, 'group_counter': 3, 'group_order': 29040, 'label': '20B7', 'order': 20, 'powers': [40, 68, 10, 71], 'representative': 42, 'size': 121}
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id: 109628523
{'aut_label': '20B3', 'centralizer': '121.a1.a1', 'counter': 73, 'group_counter': 3, 'group_order': 29040, 'label': '20B-7', 'order': 20, 'powers': [39, 69, 9, 70], 'representative': 78, 'size': 121}
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id: 109628524
{'aut_label': '20B-1', 'centralizer': '121.a1.a1', 'counter': 74, 'group_counter': 3, 'group_order': 29040, 'label': '20B9', 'order': 20, 'powers': [38, 72, 9, 69], 'representative': 54, 'size': 121}
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id: 109628525
{'aut_label': '20B1', 'centralizer': '121.a1.a1', 'counter': 75, 'group_counter': 3, 'group_order': 29040, 'label': '20B-9', 'order': 20, 'powers': [37, 73, 10, 68], 'representative': 66, 'size': 121}
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id: 109628526
{'aut_label': '22A', 'centralizer': '40.a1.a1', 'counter': 76, 'group_counter': 3, 'group_order': 29040, 'label': '22A', 'order': 22, 'powers': [41, 76, 76, 2], 'representative': 3960, 'size': 40}
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id: 109628527
{'aut_label': '22A', 'centralizer': '40.a1.a1', 'counter': 77, 'group_counter': 3, 'group_order': 29040, 'label': '22B', 'order': 22, 'powers': [42, 77, 77, 2], 'representative': 4320, 'size': 40}
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id: 109628528
{'aut_label': '22A', 'centralizer': '40.a1.a1', 'counter': 78, 'group_counter': 3, 'group_order': 29040, 'label': '22C', 'order': 22, 'powers': [43, 78, 78, 2], 'representative': 4440, 'size': 40}
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id: 109628529
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 79, 'group_counter': 3, 'group_order': 29040, 'label': '24A1', 'order': 24, 'powers': [48, 21, 81, 85], 'representative': 5, 'size': 121}
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id: 109628531
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 80, 'group_counter': 3, 'group_order': 29040, 'label': '24A-1', 'order': 24, 'powers': [49, 22, 82, 86], 'representative': 115, 'size': 121}
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id: 109628532
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 81, 'group_counter': 3, 'group_order': 29040, 'label': '24A5', 'order': 24, 'powers': [50, 24, 79, 83], 'representative': 25, 'size': 121}
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id: 109628533
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 82, 'group_counter': 3, 'group_order': 29040, 'label': '24A-5', 'order': 24, 'powers': [51, 23, 80, 84], 'representative': 95, 'size': 121}
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id: 109628534
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 83, 'group_counter': 3, 'group_order': 29040, 'label': '24A7', 'order': 24, 'powers': [51, 22, 85, 81], 'representative': 35, 'size': 121}
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id: 109628535
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 84, 'group_counter': 3, 'group_order': 29040, 'label': '24A-7', 'order': 24, 'powers': [50, 21, 86, 82], 'representative': 85, 'size': 121}
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id: 109628536
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 85, 'group_counter': 3, 'group_order': 29040, 'label': '24A11', 'order': 24, 'powers': [49, 23, 83, 79], 'representative': 55, 'size': 121}
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id: 109628537
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 86, 'group_counter': 3, 'group_order': 29040, 'label': '24A-11', 'order': 24, 'powers': [48, 24, 84, 80], 'representative': 65, 'size': 121}
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id: 109628538
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 87, 'group_counter': 3, 'group_order': 29040, 'label': '24B1', 'order': 24, 'powers': [48, 25, 89, 93], 'representative': 23285, 'size': 121}
-
id: 109628539
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 88, 'group_counter': 3, 'group_order': 29040, 'label': '24B-1', 'order': 24, 'powers': [49, 26, 90, 94], 'representative': 7675, 'size': 121}
-
id: 109628540
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 89, 'group_counter': 3, 'group_order': 29040, 'label': '24B5', 'order': 24, 'powers': [50, 28, 87, 91], 'representative': 25225, 'size': 121}
-
id: 109628542
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 90, 'group_counter': 3, 'group_order': 29040, 'label': '24B-5', 'order': 24, 'powers': [51, 27, 88, 92], 'representative': 11975, 'size': 121}
-
id: 109628543
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 91, 'group_counter': 3, 'group_order': 29040, 'label': '24B7', 'order': 24, 'powers': [51, 26, 93, 89], 'representative': 7595, 'size': 121}
-
id: 109628544
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 92, 'group_counter': 3, 'group_order': 29040, 'label': '24B-7', 'order': 24, 'powers': [50, 25, 94, 90], 'representative': 23365, 'size': 121}
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id: 109628545
{'aut_label': '24A1', 'centralizer': '121.a1.a1', 'counter': 93, 'group_counter': 3, 'group_order': 29040, 'label': '24B11', 'order': 24, 'powers': [49, 27, 91, 87], 'representative': 11935, 'size': 121}
-
id: 109628546
{'aut_label': '24A-1', 'centralizer': '121.a1.a1', 'counter': 94, 'group_counter': 3, 'group_order': 29040, 'label': '24B-11', 'order': 24, 'powers': [48, 28, 92, 88], 'representative': 25265, 'size': 121}
-
id: 109628547
{'aut_label': '30A1', 'centralizer': '121.a1.a1', 'counter': 95, 'group_counter': 3, 'group_order': 29040, 'label': '30A1', 'order': 30, 'powers': [52, 29, 15, 99], 'representative': 1328, 'size': 121}
-
id: 109628548
{'aut_label': '30A-1', 'centralizer': '121.a1.a1', 'counter': 96, 'group_counter': 3, 'group_order': 29040, 'label': '30A-1', 'order': 30, 'powers': [53, 30, 16, 100], 'representative': 1432, 'size': 121}
-
id: 109628549
{'aut_label': '30A7', 'centralizer': '121.a1.a1', 'counter': 97, 'group_counter': 3, 'group_order': 29040, 'label': '30A7', 'order': 30, 'powers': [58, 32, 15, 102], 'representative': 1376, 'size': 121}
-
id: 109628550
{'aut_label': '30A-7', 'centralizer': '121.a1.a1', 'counter': 98, 'group_counter': 3, 'group_order': 29040, 'label': '30A-7', 'order': 30, 'powers': [59, 31, 16, 101], 'representative': 1384, 'size': 121}
-
id: 109628551
{'aut_label': '30A1', 'centralizer': '121.a1.a1', 'counter': 99, 'group_counter': 3, 'group_order': 29040, 'label': '30A11', 'order': 30, 'powers': [57, 29, 16, 95], 'representative': 1408, 'size': 121}
-
id: 109628296
{'aut_label': '30A-1', 'centralizer': '121.a1.a1', 'counter': 100, 'group_counter': 3, 'group_order': 29040, 'label': '30A-11', 'order': 30, 'powers': [56, 30, 15, 96], 'representative': 1352, 'size': 121}
-
id: 109628297
{'aut_label': '30A-7', 'centralizer': '121.a1.a1', 'counter': 101, 'group_counter': 3, 'group_order': 29040, 'label': '30A13', 'order': 30, 'powers': [55, 31, 15, 98], 'representative': 1424, 'size': 121}
-
id: 109628298
{'aut_label': '30A7', 'centralizer': '121.a1.a1', 'counter': 102, 'group_counter': 3, 'group_order': 29040, 'label': '30A-13', 'order': 30, 'powers': [54, 32, 16, 97], 'representative': 1336, 'size': 121}
-
id: 109628299
{'aut_label': '30B1', 'centralizer': '121.a1.a1', 'counter': 103, 'group_counter': 3, 'group_order': 29040, 'label': '30B1', 'order': 30, 'powers': [59, 33, 17, 107], 'representative': 1324, 'size': 121}
-
id: 109628300
{'aut_label': '30B-1', 'centralizer': '121.a1.a1', 'counter': 104, 'group_counter': 3, 'group_order': 29040, 'label': '30B-1', 'order': 30, 'powers': [58, 34, 18, 108], 'representative': 1436, 'size': 121}
-
id: 109628301
{'aut_label': '30B7', 'centralizer': '121.a1.a1', 'counter': 105, 'group_counter': 3, 'group_order': 29040, 'label': '30B7', 'order': 30, 'powers': [57, 36, 17, 110], 'representative': 1348, 'size': 121}
-
id: 109628302
{'aut_label': '30B-7', 'centralizer': '121.a1.a1', 'counter': 106, 'group_counter': 3, 'group_order': 29040, 'label': '30B-7', 'order': 30, 'powers': [56, 35, 18, 109], 'representative': 1412, 'size': 121}
-
id: 109628303
{'aut_label': '30B1', 'centralizer': '121.a1.a1', 'counter': 107, 'group_counter': 3, 'group_order': 29040, 'label': '30B11', 'order': 30, 'powers': [55, 33, 18, 103], 'representative': 1364, 'size': 121}
-
id: 109628304
{'aut_label': '30B-1', 'centralizer': '121.a1.a1', 'counter': 108, 'group_counter': 3, 'group_order': 29040, 'label': '30B-11', 'order': 30, 'powers': [54, 34, 17, 104], 'representative': 1396, 'size': 121}
-
id: 109628305
{'aut_label': '30B-7', 'centralizer': '121.a1.a1', 'counter': 109, 'group_counter': 3, 'group_order': 29040, 'label': '30B13', 'order': 30, 'powers': [53, 35, 17, 106], 'representative': 1372, 'size': 121}
-
id: 109628307
{'aut_label': '30B7', 'centralizer': '121.a1.a1', 'counter': 110, 'group_counter': 3, 'group_order': 29040, 'label': '30B-13', 'order': 30, 'powers': [52, 36, 18, 105], 'representative': 1388, 'size': 121}
-
id: 109628308
{'aut_label': '30C1', 'centralizer': '121.a1.a1', 'counter': 111, 'group_counter': 3, 'group_order': 29040, 'label': '30C1', 'order': 30, 'powers': [59, 37, 19, 115], 'representative': 15964, 'size': 121}
-
id: 109628309
{'aut_label': '30C-1', 'centralizer': '121.a1.a1', 'counter': 112, 'group_counter': 3, 'group_order': 29040, 'label': '30C-1', 'order': 30, 'powers': [58, 38, 20, 116], 'representative': 21836, 'size': 121}
-
id: 109628310
{'aut_label': '30C7', 'centralizer': '121.a1.a1', 'counter': 113, 'group_counter': 3, 'group_order': 29040, 'label': '30C7', 'order': 30, 'powers': [57, 40, 19, 118], 'representative': 8668, 'size': 121}
-
id: 109628311
{'aut_label': '30C-7', 'centralizer': '121.a1.a1', 'counter': 114, 'group_counter': 3, 'group_order': 29040, 'label': '30C-7', 'order': 30, 'powers': [56, 39, 20, 117], 'representative': 24692, 'size': 121}
-
id: 109628312
{'aut_label': '30C1', 'centralizer': '121.a1.a1', 'counter': 115, 'group_counter': 3, 'group_order': 29040, 'label': '30C11', 'order': 30, 'powers': [55, 37, 20, 111], 'representative': 16004, 'size': 121}
-
id: 109628313
{'aut_label': '30C-1', 'centralizer': '121.a1.a1', 'counter': 116, 'group_counter': 3, 'group_order': 29040, 'label': '30C-11', 'order': 30, 'powers': [54, 38, 19, 112], 'representative': 21796, 'size': 121}
-
id: 109628314
{'aut_label': '30C-7', 'centralizer': '121.a1.a1', 'counter': 117, 'group_counter': 3, 'group_order': 29040, 'label': '30C13', 'order': 30, 'powers': [53, 39, 19, 114], 'representative': 24652, 'size': 121}
-
id: 109628315
{'aut_label': '30C7', 'centralizer': '121.a1.a1', 'counter': 118, 'group_counter': 3, 'group_order': 29040, 'label': '30C-13', 'order': 30, 'powers': [52, 40, 20, 113], 'representative': 8708, 'size': 121}
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id: 109628316
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 119, 'group_counter': 3, 'group_order': 29040, 'label': '33A1', 'order': 33, 'powers': [120, 41, 120, 6], 'representative': 2720, 'size': 40}
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id: 109628318
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 120, 'group_counter': 3, 'group_order': 29040, 'label': '33A-1', 'order': 33, 'powers': [119, 41, 119, 5], 'representative': 26440, 'size': 40}
-
id: 109628319
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 121, 'group_counter': 3, 'group_order': 29040, 'label': '33B1', 'order': 33, 'powers': [122, 42, 122, 6], 'representative': 2960, 'size': 40}
-
id: 109628320
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 122, 'group_counter': 3, 'group_order': 29040, 'label': '33B-1', 'order': 33, 'powers': [121, 42, 121, 5], 'representative': 27520, 'size': 40}
-
id: 109628321
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 123, 'group_counter': 3, 'group_order': 29040, 'label': '33C1', 'order': 33, 'powers': [124, 43, 124, 6], 'representative': 3920, 'size': 40}
-
id: 109628322
{'aut_label': '33A1', 'centralizer': '40.a1.a1', 'counter': 124, 'group_counter': 3, 'group_order': 29040, 'label': '33C-1', 'order': 33, 'powers': [123, 43, 123, 5], 'representative': 26560, 'size': 40}
-
id: 109628323
{'aut_label': '40A1', 'centralizer': '121.a1.a1', 'counter': 125, 'group_counter': 3, 'group_order': 29040, 'label': '40A1', 'order': 40, 'powers': [68, 127, 21, 133], 'representative': 3, 'size': 121}
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id: 109628324
{'aut_label': '40A-1', 'centralizer': '121.a1.a1', 'counter': 126, 'group_counter': 3, 'group_order': 29040, 'label': '40A-1', 'order': 40, 'powers': [69, 128, 22, 134], 'representative': 117, 'size': 121}
-
id: 109628325
{'aut_label': '40A3', 'centralizer': '121.a1.a1', 'counter': 127, 'group_counter': 3, 'group_order': 29040, 'label': '40A3', 'order': 40, 'powers': [70, 131, 23, 130], 'representative': 9, 'size': 121}
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id: 109628326
{'aut_label': '40A-3', 'centralizer': '121.a1.a1', 'counter': 128, 'group_counter': 3, 'group_order': 29040, 'label': '40A-3', 'order': 40, 'powers': [71, 132, 24, 129], 'representative': 111, 'size': 121}
-
id: 109628327
{'aut_label': '40A-3', 'centralizer': '121.a1.a1', 'counter': 129, 'group_counter': 3, 'group_order': 29040, 'label': '40A7', 'order': 40, 'powers': [72, 140, 22, 128], 'representative': 21, 'size': 121}
-
id: 109628329
{'aut_label': '40A3', 'centralizer': '121.a1.a1', 'counter': 130, 'group_counter': 3, 'group_order': 29040, 'label': '40A-7', 'order': 40, 'powers': [73, 139, 21, 127], 'representative': 99, 'size': 121}
-
id: 109628330
{'aut_label': '40A9', 'centralizer': '121.a1.a1', 'counter': 131, 'group_counter': 3, 'group_order': 29040, 'label': '40A9', 'order': 40, 'powers': [74, 136, 21, 139], 'representative': 27, 'size': 121}
-
id: 109628331
{'aut_label': '40A-9', 'centralizer': '121.a1.a1', 'counter': 132, 'group_counter': 3, 'group_order': 29040, 'label': '40A-9', 'order': 40, 'powers': [75, 135, 22, 140], 'representative': 93, 'size': 121}
-
id: 109628332
{'aut_label': '40A1', 'centralizer': '121.a1.a1', 'counter': 133, 'group_counter': 3, 'group_order': 29040, 'label': '40A11', 'order': 40, 'powers': [75, 130, 23, 125], 'representative': 33, 'size': 121}
-
id: 109628333
{'aut_label': '40A-1', 'centralizer': '121.a1.a1', 'counter': 134, 'group_counter': 3, 'group_order': 29040, 'label': '40A-11', 'order': 40, 'powers': [74, 129, 24, 126], 'representative': 87, 'size': 121}
-
id: 109628334
{'aut_label': '40A13', 'centralizer': '121.a1.a1', 'counter': 135, 'group_counter': 3, 'group_order': 29040, 'label': '40A13', 'order': 40, 'powers': [73, 126, 24, 138], 'representative': 39, 'size': 121}
-
id: 109628335
{'aut_label': '40A-13', 'centralizer': '121.a1.a1', 'counter': 136, 'group_counter': 3, 'group_order': 29040, 'label': '40A-13', 'order': 40, 'powers': [72, 125, 23, 137], 'representative': 81, 'size': 121}
-
id: 109628336
{'aut_label': '40A-13', 'centralizer': '121.a1.a1', 'counter': 137, 'group_counter': 3, 'group_order': 29040, 'label': '40A17', 'order': 40, 'powers': [71, 133, 21, 136], 'representative': 51, 'size': 121}
-
id: 109628337
{'aut_label': '40A13', 'centralizer': '121.a1.a1', 'counter': 138, 'group_counter': 3, 'group_order': 29040, 'label': '40A-17', 'order': 40, 'powers': [70, 134, 22, 135], 'representative': 69, 'size': 121}
-
id: 109628338
{'aut_label': '40A9', 'centralizer': '121.a1.a1', 'counter': 139, 'group_counter': 3, 'group_order': 29040, 'label': '40A19', 'order': 40, 'powers': [69, 137, 23, 131], 'representative': 57, 'size': 121}
-
id: 109628340
{'aut_label': '40A-9', 'centralizer': '121.a1.a1', 'counter': 140, 'group_counter': 3, 'group_order': 29040, 'label': '40A-19', 'order': 40, 'powers': [68, 138, 24, 132], 'representative': 63, 'size': 121}
-
id: 109628341
{'aut_label': '40A1', 'centralizer': '121.a1.a1', 'counter': 141, 'group_counter': 3, 'group_order': 29040, 'label': '40B1', 'order': 40, 'powers': [68, 143, 25, 149], 'representative': 28803, 'size': 121}
-
id: 109628342
{'aut_label': '40A-1', 'centralizer': '121.a1.a1', 'counter': 142, 'group_counter': 3, 'group_order': 29040, 'label': '40B-1', 'order': 40, 'powers': [69, 144, 26, 150], 'representative': 20157, 'size': 121}
-
id: 109628343
{'aut_label': '40A3', 'centralizer': '121.a1.a1', 'counter': 143, 'group_counter': 3, 'group_order': 29040, 'label': '40B3', 'order': 40, 'powers': [70, 147, 27, 146], 'representative': 7809, 'size': 121}
-
id: 109628344
{'aut_label': '40A-3', 'centralizer': '121.a1.a1', 'counter': 144, 'group_counter': 3, 'group_order': 29040, 'label': '40B-3', 'order': 40, 'powers': [71, 148, 28, 145], 'representative': 23271, 'size': 121}
-
id: 109628345
{'aut_label': '40A-3', 'centralizer': '121.a1.a1', 'counter': 145, 'group_counter': 3, 'group_order': 29040, 'label': '40B7', 'order': 40, 'powers': [72, 156, 26, 144], 'representative': 18141, 'size': 121}
-
id: 109628346
{'aut_label': '40A3', 'centralizer': '121.a1.a1', 'counter': 146, 'group_counter': 3, 'group_order': 29040, 'label': '40B-7', 'order': 40, 'powers': [73, 155, 25, 143], 'representative': 15459, 'size': 121}
-
id: 109628347
{'aut_label': '40A9', 'centralizer': '121.a1.a1', 'counter': 147, 'group_counter': 3, 'group_order': 29040, 'label': '40B9', 'order': 40, 'powers': [74, 152, 25, 155], 'representative': 1947, 'size': 121}
-
id: 109628348
{'aut_label': '40A-9', 'centralizer': '121.a1.a1', 'counter': 148, 'group_counter': 3, 'group_order': 29040, 'label': '40B-9', 'order': 40, 'powers': [75, 151, 26, 156], 'representative': 4653, 'size': 121}
-
id: 109628349
{'aut_label': '40A1', 'centralizer': '121.a1.a1', 'counter': 149, 'group_counter': 3, 'group_order': 29040, 'label': '40B11', 'order': 40, 'powers': [75, 146, 27, 141], 'representative': 14913, 'size': 121}
-
id: 109628351
{'aut_label': '40A-1', 'centralizer': '121.a1.a1', 'counter': 150, 'group_counter': 3, 'group_order': 29040, 'label': '40B-11', 'order': 40, 'powers': [74, 145, 28, 142], 'representative': 17607, 'size': 121}
-
id: 109628352
{'aut_label': '40A13', 'centralizer': '121.a1.a1', 'counter': 151, 'group_counter': 3, 'group_order': 29040, 'label': '40B13', 'order': 40, 'powers': [73, 142, 28, 154], 'representative': 4119, 'size': 121}
-
id: 109628353
{'aut_label': '40A-13', 'centralizer': '121.a1.a1', 'counter': 152, 'group_counter': 3, 'group_order': 29040, 'label': '40B-13', 'order': 40, 'powers': [72, 141, 27, 153], 'representative': 1401, 'size': 121}
-
id: 109628354
{'aut_label': '40A-13', 'centralizer': '121.a1.a1', 'counter': 153, 'group_counter': 3, 'group_order': 29040, 'label': '40B17', 'order': 40, 'powers': [71, 149, 25, 152], 'representative': 25371, 'size': 121}
-
id: 109628355
{'aut_label': '40A13', 'centralizer': '121.a1.a1', 'counter': 154, 'group_counter': 3, 'group_order': 29040, 'label': '40B-17', 'order': 40, 'powers': [70, 150, 26, 151], 'representative': 13029, 'size': 121}
-
id: 109628356
{'aut_label': '40A9', 'centralizer': '121.a1.a1', 'counter': 155, 'group_counter': 3, 'group_order': 29040, 'label': '40B19', 'order': 40, 'powers': [69, 153, 27, 147], 'representative': 28497, 'size': 121}
-
id: 109628357
{'aut_label': '40A-9', 'centralizer': '121.a1.a1', 'counter': 156, 'group_counter': 3, 'group_order': 29040, 'label': '40B-19', 'order': 40, 'powers': [68, 154, 28, 148], 'representative': 21063, 'size': 121}
-
id: 109628358
{'aut_label': '60A1', 'centralizer': '121.a1.a1', 'counter': 157, 'group_counter': 3, 'group_order': 29040, 'label': '60A1', 'order': 60, 'powers': [111, 60, 44, 161], 'representative': 1322, 'size': 121}
-
id: 109628359
{'aut_label': '60A-1', 'centralizer': '121.a1.a1', 'counter': 158, 'group_counter': 3, 'group_order': 29040, 'label': '60A-1', 'order': 60, 'powers': [112, 61, 45, 162], 'representative': 1438, 'size': 121}
-
id: 109628360
{'aut_label': '60A7', 'centralizer': '121.a1.a1', 'counter': 159, 'group_counter': 3, 'group_order': 29040, 'label': '60A7', 'order': 60, 'powers': [113, 64, 47, 165], 'representative': 1334, 'size': 121}
-
id: 109628362
{'aut_label': '60A-7', 'centralizer': '121.a1.a1', 'counter': 160, 'group_counter': 3, 'group_order': 29040, 'label': '60A-7', 'order': 60, 'powers': [114, 65, 46, 166], 'representative': 1426, 'size': 121}
-
id: 109628363
{'aut_label': '60A1', 'centralizer': '121.a1.a1', 'counter': 161, 'group_counter': 3, 'group_order': 29040, 'label': '60A11', 'order': 60, 'powers': [115, 67, 45, 157], 'representative': 1342, 'size': 121}
-
id: 109628364
{'aut_label': '60A-1', 'centralizer': '121.a1.a1', 'counter': 162, 'group_counter': 3, 'group_order': 29040, 'label': '60A-11', 'order': 60, 'powers': [116, 66, 44, 158], 'representative': 1418, 'size': 121}
-
id: 109628365
{'aut_label': '60A-7', 'centralizer': '121.a1.a1', 'counter': 163, 'group_counter': 3, 'group_order': 29040, 'label': '60A13', 'order': 60, 'powers': [117, 65, 44, 169], 'representative': 1346, 'size': 121}
-
id: 109628366
{'aut_label': '60A7', 'centralizer': '121.a1.a1', 'counter': 164, 'group_counter': 3, 'group_order': 29040, 'label': '60A-13', 'order': 60, 'powers': [118, 64, 45, 170], 'representative': 1414, 'size': 121}
-
id: 109628367
{'aut_label': '60A7', 'centralizer': '121.a1.a1', 'counter': 165, 'group_counter': 3, 'group_order': 29040, 'label': '60A17', 'order': 60, 'powers': [118, 63, 46, 159], 'representative': 1354, 'size': 121}
-
id: 109628368
{'aut_label': '60A-7', 'centralizer': '121.a1.a1', 'counter': 166, 'group_counter': 3, 'group_order': 29040, 'label': '60A-17', 'order': 60, 'powers': [117, 62, 47, 160], 'representative': 1406, 'size': 121}
-
id: 109628369
{'aut_label': '60A-1', 'centralizer': '121.a1.a1', 'counter': 167, 'group_counter': 3, 'group_order': 29040, 'label': '60A19', 'order': 60, 'powers': [116, 61, 47, 171], 'representative': 1358, 'size': 121}
-
id: 109628370
{'aut_label': '60A1', 'centralizer': '121.a1.a1', 'counter': 168, 'group_counter': 3, 'group_order': 29040, 'label': '60A-19', 'order': 60, 'powers': [115, 60, 46, 172], 'representative': 1402, 'size': 121}
-
id: 109628371
{'aut_label': '60A-7', 'centralizer': '121.a1.a1', 'counter': 169, 'group_counter': 3, 'group_order': 29040, 'label': '60A23', 'order': 60, 'powers': [114, 62, 45, 163], 'representative': 1366, 'size': 121}
-
id: 109628373
{'aut_label': '60A7', 'centralizer': '121.a1.a1', 'counter': 170, 'group_counter': 3, 'group_order': 29040, 'label': '60A-23', 'order': 60, 'powers': [113, 63, 44, 164], 'representative': 1394, 'size': 121}
-
id: 109628374
{'aut_label': '60A-1', 'centralizer': '121.a1.a1', 'counter': 171, 'group_counter': 3, 'group_order': 29040, 'label': '60A29', 'order': 60, 'powers': [112, 66, 46, 167], 'representative': 1378, 'size': 121}
-
id: 109628375
{'aut_label': '60A1', 'centralizer': '121.a1.a1', 'counter': 172, 'group_counter': 3, 'group_order': 29040, 'label': '60A-29', 'order': 60, 'powers': [111, 67, 47, 168], 'representative': 1382, 'size': 121}
-
id: 109628376
{'aut_label': '60B1', 'centralizer': '121.a1.a1', 'counter': 173, 'group_counter': 3, 'group_order': 29040, 'label': '60B1', 'order': 60, 'powers': [111, 68, 48, 177], 'representative': 2, 'size': 121}
-
id: 109628377
{'aut_label': '60B-1', 'centralizer': '121.a1.a1', 'counter': 174, 'group_counter': 3, 'group_order': 29040, 'label': '60B-1', 'order': 60, 'powers': [112, 69, 49, 178], 'representative': 118, 'size': 121}
-
id: 109628378
{'aut_label': '60B7', 'centralizer': '121.a1.a1', 'counter': 175, 'group_counter': 3, 'group_order': 29040, 'label': '60B7', 'order': 60, 'powers': [113, 72, 51, 181], 'representative': 14, 'size': 121}
-
id: 109628379
{'aut_label': '60B-7', 'centralizer': '121.a1.a1', 'counter': 176, 'group_counter': 3, 'group_order': 29040, 'label': '60B-7', 'order': 60, 'powers': [114, 73, 50, 182], 'representative': 106, 'size': 121}
-
id: 109628380
{'aut_label': '60B1', 'centralizer': '121.a1.a1', 'counter': 177, 'group_counter': 3, 'group_order': 29040, 'label': '60B11', 'order': 60, 'powers': [115, 75, 49, 173], 'representative': 22, 'size': 121}
-
id: 109628381
{'aut_label': '60B-1', 'centralizer': '121.a1.a1', 'counter': 178, 'group_counter': 3, 'group_order': 29040, 'label': '60B-11', 'order': 60, 'powers': [116, 74, 48, 174], 'representative': 98, 'size': 121}
-
id: 109628382
{'aut_label': '60B-7', 'centralizer': '121.a1.a1', 'counter': 179, 'group_counter': 3, 'group_order': 29040, 'label': '60B13', 'order': 60, 'powers': [117, 73, 48, 185], 'representative': 26, 'size': 121}
-
id: 109628384
{'aut_label': '60B7', 'centralizer': '121.a1.a1', 'counter': 180, 'group_counter': 3, 'group_order': 29040, 'label': '60B-13', 'order': 60, 'powers': [118, 72, 49, 186], 'representative': 94, 'size': 121}
-
id: 109628385
{'aut_label': '60B7', 'centralizer': '121.a1.a1', 'counter': 181, 'group_counter': 3, 'group_order': 29040, 'label': '60B17', 'order': 60, 'powers': [118, 71, 50, 175], 'representative': 34, 'size': 121}
-
id: 109628386
{'aut_label': '60B-7', 'centralizer': '121.a1.a1', 'counter': 182, 'group_counter': 3, 'group_order': 29040, 'label': '60B-17', 'order': 60, 'powers': [117, 70, 51, 176], 'representative': 86, 'size': 121}
-
id: 109628387
{'aut_label': '60B-1', 'centralizer': '121.a1.a1', 'counter': 183, 'group_counter': 3, 'group_order': 29040, 'label': '60B19', 'order': 60, 'powers': [116, 69, 51, 187], 'representative': 38, 'size': 121}
-
id: 109628388
{'aut_label': '60B1', 'centralizer': '121.a1.a1', 'counter': 184, 'group_counter': 3, 'group_order': 29040, 'label': '60B-19', 'order': 60, 'powers': [115, 68, 50, 188], 'representative': 82, 'size': 121}
-
id: 109628389
{'aut_label': '60B-7', 'centralizer': '121.a1.a1', 'counter': 185, 'group_counter': 3, 'group_order': 29040, 'label': '60B23', 'order': 60, 'powers': [114, 70, 49, 179], 'representative': 46, 'size': 121}
-
id: 109628390
{'aut_label': '60B7', 'centralizer': '121.a1.a1', 'counter': 186, 'group_counter': 3, 'group_order': 29040, 'label': '60B-23', 'order': 60, 'powers': [113, 71, 48, 180], 'representative': 74, 'size': 121}
-
id: 109628391
{'aut_label': '60B-1', 'centralizer': '121.a1.a1', 'counter': 187, 'group_counter': 3, 'group_order': 29040, 'label': '60B29', 'order': 60, 'powers': [112, 74, 50, 183], 'representative': 58, 'size': 121}
-
id: 109628392
{'aut_label': '60B1', 'centralizer': '121.a1.a1', 'counter': 188, 'group_counter': 3, 'group_order': 29040, 'label': '60B-29', 'order': 60, 'powers': [111, 75, 51, 184], 'representative': 62, 'size': 121}
-
id: 109628393
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 189, 'group_counter': 3, 'group_order': 29040, 'label': '66A1', 'order': 66, 'powers': [119, 76, 190, 16], 'representative': 1360, 'size': 40}
-
id: 109628395
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 190, 'group_counter': 3, 'group_order': 29040, 'label': '66A-1', 'order': 66, 'powers': [120, 76, 189, 15], 'representative': 1400, 'size': 40}
-
id: 109628396
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 191, 'group_counter': 3, 'group_order': 29040, 'label': '66B1', 'order': 66, 'powers': [121, 77, 192, 16], 'representative': 1480, 'size': 40}
-
id: 109628397
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 192, 'group_counter': 3, 'group_order': 29040, 'label': '66B-1', 'order': 66, 'powers': [122, 77, 191, 15], 'representative': 1520, 'size': 40}
-
id: 109628398
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 193, 'group_counter': 3, 'group_order': 29040, 'label': '66C1', 'order': 66, 'powers': [123, 78, 194, 16], 'representative': 1960, 'size': 40}
-
id: 109628399
{'aut_label': '66A1', 'centralizer': '40.a1.a1', 'counter': 194, 'group_counter': 3, 'group_order': 29040, 'label': '66C-1', 'order': 66, 'powers': [124, 78, 193, 15], 'representative': 2000, 'size': 40}
-
id: 109628400
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 195, 'group_counter': 3, 'group_order': 29040, 'label': '120A1', 'order': 120, 'powers': [173, 125, 79, 199], 'representative': 1, 'size': 121}
-
id: 109628401
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 196, 'group_counter': 3, 'group_order': 29040, 'label': '120A-1', 'order': 120, 'powers': [174, 126, 80, 200], 'representative': 119, 'size': 121}
-
id: 109628402
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 197, 'group_counter': 3, 'group_order': 29040, 'label': '120A7', 'order': 120, 'powers': [175, 129, 83, 218], 'representative': 7, 'size': 121}
-
id: 109628403
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 198, 'group_counter': 3, 'group_order': 29040, 'label': '120A-7', 'order': 120, 'powers': [176, 130, 84, 217], 'representative': 113, 'size': 121}
-
id: 109628404
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 199, 'group_counter': 3, 'group_order': 29040, 'label': '120A11', 'order': 120, 'powers': [177, 133, 85, 195], 'representative': 11, 'size': 121}
-
id: 109628407
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 200, 'group_counter': 3, 'group_order': 29040, 'label': '120A-11', 'order': 120, 'powers': [178, 134, 86, 196], 'representative': 109, 'size': 121}
-
id: 109628408
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 201, 'group_counter': 3, 'group_order': 29040, 'label': '120A13', 'order': 120, 'powers': [179, 135, 86, 207], 'representative': 13, 'size': 121}
-
id: 109628409
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 202, 'group_counter': 3, 'group_order': 29040, 'label': '120A-13', 'order': 120, 'powers': [180, 136, 85, 208], 'representative': 107, 'size': 121}
-
id: 109628410
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 203, 'group_counter': 3, 'group_order': 29040, 'label': '120A17', 'order': 120, 'powers': [181, 137, 84, 224], 'representative': 17, 'size': 121}
-
id: 109628411
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 204, 'group_counter': 3, 'group_order': 29040, 'label': '120A-17', 'order': 120, 'powers': [182, 138, 83, 223], 'representative': 103, 'size': 121}
-
id: 109628412
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 205, 'group_counter': 3, 'group_order': 29040, 'label': '120A19', 'order': 120, 'powers': [183, 139, 82, 212], 'representative': 19, 'size': 121}
-
id: 109628413
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 206, 'group_counter': 3, 'group_order': 29040, 'label': '120A-19', 'order': 120, 'powers': [184, 140, 81, 211], 'representative': 101, 'size': 121}
-
id: 109628414
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 207, 'group_counter': 3, 'group_order': 29040, 'label': '120A23', 'order': 120, 'powers': [185, 138, 80, 201], 'representative': 23, 'size': 121}
-
id: 109628415
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 208, 'group_counter': 3, 'group_order': 29040, 'label': '120A-23', 'order': 120, 'powers': [186, 137, 79, 202], 'representative': 97, 'size': 121}
-
id: 109628416
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 209, 'group_counter': 3, 'group_order': 29040, 'label': '120A29', 'order': 120, 'powers': [187, 134, 81, 216], 'representative': 29, 'size': 121}
-
id: 109628418
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 210, 'group_counter': 3, 'group_order': 29040, 'label': '120A-29', 'order': 120, 'powers': [188, 133, 82, 215], 'representative': 91, 'size': 121}
-
id: 109628419
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 211, 'group_counter': 3, 'group_order': 29040, 'label': '120A31', 'order': 120, 'powers': [188, 132, 83, 206], 'representative': 31, 'size': 121}
-
id: 109628420
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 212, 'group_counter': 3, 'group_order': 29040, 'label': '120A-31', 'order': 120, 'powers': [187, 131, 84, 205], 'representative': 89, 'size': 121}
-
id: 109628421
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 213, 'group_counter': 3, 'group_order': 29040, 'label': '120A37', 'order': 120, 'powers': [186, 128, 86, 219], 'representative': 37, 'size': 121}
-
id: 109628422
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 214, 'group_counter': 3, 'group_order': 29040, 'label': '120A-37', 'order': 120, 'powers': [185, 127, 85, 220], 'representative': 83, 'size': 121}
-
id: 109628423
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 215, 'group_counter': 3, 'group_order': 29040, 'label': '120A41', 'order': 120, 'powers': [184, 125, 84, 210], 'representative': 41, 'size': 121}
-
id: 109628424
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 216, 'group_counter': 3, 'group_order': 29040, 'label': '120A-41', 'order': 120, 'powers': [183, 126, 83, 209], 'representative': 79, 'size': 121}
-
id: 109628425
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 217, 'group_counter': 3, 'group_order': 29040, 'label': '120A43', 'order': 120, 'powers': [182, 127, 82, 198], 'representative': 43, 'size': 121}
-
id: 109628426
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 218, 'group_counter': 3, 'group_order': 29040, 'label': '120A-43', 'order': 120, 'powers': [181, 128, 81, 197], 'representative': 77, 'size': 121}
-
id: 109628427
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 219, 'group_counter': 3, 'group_order': 29040, 'label': '120A47', 'order': 120, 'powers': [180, 129, 80, 213], 'representative': 47, 'size': 121}
-
id: 109628429
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 220, 'group_counter': 3, 'group_order': 29040, 'label': '120A-47', 'order': 120, 'powers': [179, 130, 79, 214], 'representative': 73, 'size': 121}
-
id: 109628430
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 221, 'group_counter': 3, 'group_order': 29040, 'label': '120A49', 'order': 120, 'powers': [178, 131, 79, 225], 'representative': 49, 'size': 121}
-
id: 109628431
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 222, 'group_counter': 3, 'group_order': 29040, 'label': '120A-49', 'order': 120, 'powers': [177, 132, 80, 226], 'representative': 71, 'size': 121}
-
id: 109628432
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 223, 'group_counter': 3, 'group_order': 29040, 'label': '120A53', 'order': 120, 'powers': [176, 135, 81, 204], 'representative': 53, 'size': 121}
-
id: 109628433
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 224, 'group_counter': 3, 'group_order': 29040, 'label': '120A-53', 'order': 120, 'powers': [175, 136, 82, 203], 'representative': 67, 'size': 121}
-
id: 109628434
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 225, 'group_counter': 3, 'group_order': 29040, 'label': '120A59', 'order': 120, 'powers': [174, 139, 85, 221], 'representative': 59, 'size': 121}
-
id: 109628435
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 226, 'group_counter': 3, 'group_order': 29040, 'label': '120A-59', 'order': 120, 'powers': [173, 140, 86, 222], 'representative': 61, 'size': 121}
-
id: 109628436
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 227, 'group_counter': 3, 'group_order': 29040, 'label': '120B1', 'order': 120, 'powers': [173, 141, 87, 231], 'representative': 1321, 'size': 121}
-
id: 109628437
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 228, 'group_counter': 3, 'group_order': 29040, 'label': '120B-1', 'order': 120, 'powers': [174, 142, 88, 232], 'representative': 1439, 'size': 121}
-
id: 109628438
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 229, 'group_counter': 3, 'group_order': 29040, 'label': '120B7', 'order': 120, 'powers': [175, 145, 91, 250], 'representative': 1327, 'size': 121}
-
id: 109628440
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 230, 'group_counter': 3, 'group_order': 29040, 'label': '120B-7', 'order': 120, 'powers': [176, 146, 92, 249], 'representative': 1433, 'size': 121}
-
id: 109628441
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 231, 'group_counter': 3, 'group_order': 29040, 'label': '120B11', 'order': 120, 'powers': [177, 149, 93, 227], 'representative': 1331, 'size': 121}
-
id: 109628442
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 232, 'group_counter': 3, 'group_order': 29040, 'label': '120B-11', 'order': 120, 'powers': [178, 150, 94, 228], 'representative': 1429, 'size': 121}
-
id: 109628443
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 233, 'group_counter': 3, 'group_order': 29040, 'label': '120B13', 'order': 120, 'powers': [179, 151, 94, 239], 'representative': 1333, 'size': 121}
-
id: 109628444
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 234, 'group_counter': 3, 'group_order': 29040, 'label': '120B-13', 'order': 120, 'powers': [180, 152, 93, 240], 'representative': 1427, 'size': 121}
-
id: 109628445
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 235, 'group_counter': 3, 'group_order': 29040, 'label': '120B17', 'order': 120, 'powers': [181, 153, 92, 256], 'representative': 1337, 'size': 121}
-
id: 109628446
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 236, 'group_counter': 3, 'group_order': 29040, 'label': '120B-17', 'order': 120, 'powers': [182, 154, 91, 255], 'representative': 1423, 'size': 121}
-
id: 109628447
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 237, 'group_counter': 3, 'group_order': 29040, 'label': '120B19', 'order': 120, 'powers': [183, 155, 90, 244], 'representative': 1339, 'size': 121}
-
id: 109628448
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 238, 'group_counter': 3, 'group_order': 29040, 'label': '120B-19', 'order': 120, 'powers': [184, 156, 89, 243], 'representative': 1421, 'size': 121}
-
id: 109628449
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 239, 'group_counter': 3, 'group_order': 29040, 'label': '120B23', 'order': 120, 'powers': [185, 154, 88, 233], 'representative': 1343, 'size': 121}
-
id: 109628451
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 240, 'group_counter': 3, 'group_order': 29040, 'label': '120B-23', 'order': 120, 'powers': [186, 153, 87, 234], 'representative': 1417, 'size': 121}
-
id: 109628452
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 241, 'group_counter': 3, 'group_order': 29040, 'label': '120B29', 'order': 120, 'powers': [187, 150, 89, 248], 'representative': 1349, 'size': 121}
-
id: 109628453
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 242, 'group_counter': 3, 'group_order': 29040, 'label': '120B-29', 'order': 120, 'powers': [188, 149, 90, 247], 'representative': 1411, 'size': 121}
-
id: 109628454
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 243, 'group_counter': 3, 'group_order': 29040, 'label': '120B31', 'order': 120, 'powers': [188, 148, 91, 238], 'representative': 1351, 'size': 121}
-
id: 109628455
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 244, 'group_counter': 3, 'group_order': 29040, 'label': '120B-31', 'order': 120, 'powers': [187, 147, 92, 237], 'representative': 1409, 'size': 121}
-
id: 109628456
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 245, 'group_counter': 3, 'group_order': 29040, 'label': '120B37', 'order': 120, 'powers': [186, 144, 94, 251], 'representative': 1357, 'size': 121}
-
id: 109628457
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 246, 'group_counter': 3, 'group_order': 29040, 'label': '120B-37', 'order': 120, 'powers': [185, 143, 93, 252], 'representative': 1403, 'size': 121}
-
id: 109628458
{'aut_label': '120A1', 'centralizer': '121.a1.a1', 'counter': 247, 'group_counter': 3, 'group_order': 29040, 'label': '120B41', 'order': 120, 'powers': [184, 141, 92, 242], 'representative': 1361, 'size': 121}
-
id: 109628459
{'aut_label': '120A-1', 'centralizer': '121.a1.a1', 'counter': 248, 'group_counter': 3, 'group_order': 29040, 'label': '120B-41', 'order': 120, 'powers': [183, 142, 91, 241], 'representative': 1399, 'size': 121}
-
id: 109628460
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 249, 'group_counter': 3, 'group_order': 29040, 'label': '120B43', 'order': 120, 'powers': [182, 143, 90, 230], 'representative': 1363, 'size': 121}
-
id: 109628462
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 250, 'group_counter': 3, 'group_order': 29040, 'label': '120B-43', 'order': 120, 'powers': [181, 144, 89, 229], 'representative': 1397, 'size': 121}
-
id: 109628463
{'aut_label': '120A7', 'centralizer': '121.a1.a1', 'counter': 251, 'group_counter': 3, 'group_order': 29040, 'label': '120B47', 'order': 120, 'powers': [180, 145, 88, 245], 'representative': 1367, 'size': 121}
-
id: 109628464
{'aut_label': '120A-7', 'centralizer': '121.a1.a1', 'counter': 252, 'group_counter': 3, 'group_order': 29040, 'label': '120B-47', 'order': 120, 'powers': [179, 146, 87, 246], 'representative': 1393, 'size': 121}
-
id: 109628465
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 253, 'group_counter': 3, 'group_order': 29040, 'label': '120B49', 'order': 120, 'powers': [178, 147, 87, 257], 'representative': 1369, 'size': 121}
-
id: 109628466
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 254, 'group_counter': 3, 'group_order': 29040, 'label': '120B-49', 'order': 120, 'powers': [177, 148, 88, 258], 'representative': 1391, 'size': 121}
-
id: 109628467
{'aut_label': '120A13', 'centralizer': '121.a1.a1', 'counter': 255, 'group_counter': 3, 'group_order': 29040, 'label': '120B53', 'order': 120, 'powers': [176, 151, 89, 236], 'representative': 1373, 'size': 121}
-
id: 109628468
{'aut_label': '120A-13', 'centralizer': '121.a1.a1', 'counter': 256, 'group_counter': 3, 'group_order': 29040, 'label': '120B-53', 'order': 120, 'powers': [175, 152, 90, 235], 'representative': 1387, 'size': 121}
-
id: 109628469
{'aut_label': '120A19', 'centralizer': '121.a1.a1', 'counter': 257, 'group_counter': 3, 'group_order': 29040, 'label': '120B59', 'order': 120, 'powers': [174, 155, 93, 253], 'representative': 1379, 'size': 121}
-
id: 109628470
{'aut_label': '120A-19', 'centralizer': '121.a1.a1', 'counter': 258, 'group_counter': 3, 'group_order': 29040, 'label': '120B-59', 'order': 120, 'powers': [173, 156, 94, 254], 'representative': 1381, 'size': 121}
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gps_qchar • Show schema
Hide schema
-
id: 4348712
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 4348723
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 4348734
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1c', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 4348745
{'cdim': 1, 'counter': 4, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1d', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1], 'schur_index': 1}
-
id: 4348751
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id: 4348752
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id: 4348753
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id: 4348754
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id: 4348755
{'cdim': 1, 'counter': 9, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1i', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, -2, -2, 2, -1, -1, 2, 2, -2, -2, 2, 2, 2, 2, 1, 1, -1, -1, 1, 1, 2, 2, -2, -2, -2, -2, 2, 2, 2, -2, 2, -2, -2, -2, -2, -2, 2, -2, -2, 2, 2, 2, 2, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, -2, -2, -2, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, -2, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -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: 4348713
{'cdim': 1, 'counter': 10, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1j', 'multiplicity': 2, 'nt': [6, 1], 'qdim': 2, 'qvalues': [2, 2, 2, 2, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 4348714
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1k', 'multiplicity': 4, 'nt': [5, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4348715
{'cdim': 1, 'counter': 12, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1l', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, -4, 4, -4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, -4, -4, -4, -4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348716
{'cdim': 1, 'counter': 13, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1m', 'multiplicity': 4, 'nt': [8, 1], 'qdim': 4, 'qvalues': [4, 4, -4, -4, 4, 4, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 4, 4, -4, 4, 4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -4, 4, -4, 4, -4, -4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348717
{'cdim': 1, 'counter': 14, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1n', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, 4, 4, -4, -4, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 4, 4, 4, -4, 4, -4, -4, 4, 4, -4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -4, -4, -4, -4, 4, 4, 4, 4, 4, 4, -4, 4, -4, -4, 4, -4, -4, -4, -4, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 4, 4, 4, 4, 4, 4, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -4, -4, -4, -4, -4, -4, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 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: 4348718
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1o', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, 4, 4, 4, 4, -4, -4, -1, -1, -1, -1, -4, -4, 4, 4, -4, -4, 4, 4, -4, -4, -4, -4, 4, 4, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 4, 4, 4, -4, 4, -4, -4, 4, 4, -4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -4, -4, -4, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 4, -4, 4, 4, 4, 4, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 4, 4, 4, 4, 4, 4, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -4, -4, -4, -4, -4, -4, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -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: 4348719
{'cdim': 1, 'counter': 16, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1p', 'multiplicity': 4, 'nt': [10, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 4348720
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1q', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, -4, -4, 4, -2, -2, -4, -4, 4, 4, 4, 4, 4, 4, 2, 2, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, -4, -4, 4, -4, -4, 4, 4, 4, 4, -2, 2, -2, -2, 2, 2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -4, 4, -4, -4, -4, 4, -4, -4, 4, 4, -4, 4, 4, 4, -4, 4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348721
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1r', 'multiplicity': 4, 'nt': [12, 1], 'qdim': 4, 'qvalues': [4, 4, 4, 4, -2, -2, -4, -4, -4, -4, 4, 4, 4, 4, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, -2, -2, -2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348722
{'cdim': 1, 'counter': 19, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1s', 'multiplicity': 8, 'nt': [15, 1], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, -4, 8, 8, 8, 8, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, 8, 8, 8, 8, 8, 8, 8, 8, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 4348724
{'cdim': 1, 'counter': 20, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1t', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, 8, 8, -8, -8, 8, 8, -2, -2, -2, -2, -8, -8, 8, 8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 8, 8, 8, 8, -8, 8, 8, -8, -8, 8, -8, -2, -2, -2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, 2, -2, -2, -2, 2, -2, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 2, 2, -2, -2, 2, 2, 2, -2, 2, -2, -2, 2, -2, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, -2, -2, -2, -2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, -2, 2, 2, -2, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348725
{'cdim': 1, 'counter': 21, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1u', 'multiplicity': 8, 'nt': [20, 1], 'qdim': 8, 'qvalues': [8, 8, 8, 8, 8, 8, -8, -8, -8, -8, -2, -2, -2, -2, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, -8, -8, -8, -8, -8, -8, -8, -8, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348726
{'cdim': 1, 'counter': 22, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1v', 'multiplicity': 8, 'nt': [24, 1], 'qdim': 8, 'qvalues': [8, -8, 8, -8, -4, -4, 0, 0, 0, 0, 8, 8, 8, 8, 4, 4, 4, 4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, -8, 8, -8, 8, 8, 8, -8, -8, -8, -8, -8, -8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, -4, 4, -4, -4, 4, 4, -4, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348727
{'cdim': 1, 'counter': 23, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1w', 'multiplicity': 8, 'nt': [24, 1], 'qdim': 8, 'qvalues': [8, 8, -8, -8, -4, -4, 0, 0, 0, 0, 8, 8, 8, 8, -4, -4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, -8, -8, -8, -8, -8, -8, 8, 8, -8, 8, 8, -8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, -4, 4, -4, 4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 4, -4, 4, 4, 4, 4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348728
{'cdim': 1, 'counter': 24, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1x', 'multiplicity': 8, 'nt': [30, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -4, -4, 8, 8, -8, -8, -2, -2, -2, -2, 4, 4, -4, -4, 4, 4, -8, -8, 8, 8, 8, 8, -8, -8, -2, 2, -2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 8, 8, 8, 4, -4, 4, 4, -4, -4, 4, -4, 1, 1, 1, 1, 1, 1, 1, 1, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, 2, -8, -8, -8, 4, -4, -4, -4, -4, -4, -4, 4, -4, 4, 4, -4, 4, 4, 4, 4, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -4, -4, -4, -4, -4, -4, 2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 4, 4, 4, 4, 4, 4, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 4348729
{'cdim': 1, 'counter': 25, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1y', 'multiplicity': 8, 'nt': [30, 1], 'qdim': 8, 'qvalues': [8, -8, -8, 8, -4, -4, 8, 8, -8, -8, -2, -2, -2, -2, 4, 4, -4, -4, 4, 4, 8, 8, -8, -8, -8, -8, 8, 8, -2, 2, -2, 2, 2, 2, 2, 2, -2, 2, 2, -2, 8, 8, 8, 4, -4, 4, 4, -4, -4, 4, -4, 1, 1, 1, 1, 1, 1, 1, 1, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, -2, 2, 2, 2, -2, 2, -8, -8, -8, -4, 4, 4, 4, 4, 4, 4, -4, 4, -4, -4, 4, -4, -4, -4, -4, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -4, -4, -4, -4, -4, -4, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, -2, 2, -2, 2, 2, 2, -2, 2, -2, -2, 2, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, -1, 4, 4, 4, 4, 4, 4, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1], 'schur_index': 1}
-
id: 4348730
{'cdim': 1, 'counter': 26, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1z', 'multiplicity': 8, 'nt': [30, 1], 'qdim': 8, 'qvalues': [8, 8, 8, 8, -4, -4, 8, 8, 8, 8, -2, -2, -2, -2, -4, -4, -4, -4, -4, -4, -8, -8, -8, -8, -8, -8, -8, -8, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, -4, -4, -4, -4, -4, -4, -4, -4, 1, 1, 1, 1, 1, 1, 1, 1, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, 8, 8, 8, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -4, -4, -4, -4, -4, -4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 4348731
{'cdim': 1, 'counter': 27, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1aa', 'multiplicity': 16, 'nt': [40, 1], 'qdim': 16, 'qvalues': [16, -16, 16, -16, 16, 16, 0, 0, 0, 0, -4, -4, -4, -4, -16, -16, -16, -16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, 4, -4, -4, -4, 4, 4, 4, 4, 4, 4, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -4, -4, 4, 4, -4, 4, -4, -4, 4, 4, -4, 4, 4, 4, 4, -4, 4, 4, 4, 4, -4, 4, 16, 16, 16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -16, -16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348732
{'cdim': 1, 'counter': 28, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1ab', 'multiplicity': 16, 'nt': [40, 1], 'qdim': 16, 'qvalues': [16, 16, -16, -16, 16, 16, 0, 0, 0, 0, -4, -4, -4, -4, 16, 16, -16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, -4, -4, 4, -4, -4, 4, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, 4, 4, 4, -4, 4, -4, 4, 4, -4, -4, 4, 4, 4, -4, -4, 4, 4, -4, 4, 4, 4, 4, 16, 16, 16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348733
{'cdim': 1, 'counter': 29, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1ac', 'multiplicity': 16, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, -16, -16, 16, -8, -8, -16, -16, 16, 16, -4, -4, -4, -4, 8, 8, -8, -8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, -4, 4, -4, 4, 4, 4, 4, 4, -4, 4, 4, -4, 16, 16, 16, -8, 8, -8, -8, 8, 8, -8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 4, -4, 4, 4, 4, -4, 4, 4, -4, -4, 4, -4, -4, -4, 4, -4, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 2, -2, -2, 2, -2, -2, -2, -2, -2, -2, -2, -2, 2, 2, -2, -2, -2, 2, -2, 2, 2, -2, 2, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, 2, 2, 2, 2, 2, -2, 2, -2, -2, -2, 2, -2, -2, 2, 2, 2, -2, 2, 2, -2, 2, -2, 2, -2, -2, 2, -2, -2, 2, 8, 8, 8, 8, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348735
{'cdim': 1, 'counter': 30, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1ad', 'multiplicity': 16, 'nt': [60, 0], 'qdim': 16, 'qvalues': [16, 16, 16, 16, -8, -8, -16, -16, -16, -16, -4, -4, -4, -4, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, -4, 16, 16, 16, 8, 8, 8, 8, 8, 8, 8, 8, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -8, -8, -8, -8, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348736
{'cdim': 1, 'counter': 31, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1ae', 'multiplicity': 32, 'nt': [120, 0], 'qdim': 32, 'qvalues': [32, -32, 32, -32, -16, -16, 0, 0, 0, 0, -8, -8, -8, -8, 16, 16, 16, 16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 8, -8, 8, -8, -8, -8, 8, 8, 8, 8, 8, 8, 32, 32, 32, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -32, -32, -32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 4, 4, -4, -4, 4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, 4, -4, -4, -4, -4, 4, -4, -16, -16, -16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 16, 16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348737
{'cdim': 1, 'counter': 32, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.1af', 'multiplicity': 32, 'nt': [120, 0], 'qdim': 32, 'qvalues': [32, 32, -32, -32, -16, -16, 0, 0, 0, 0, -8, -8, -8, -8, -16, -16, 16, 16, 16, 16, 0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 8, 8, 8, 8, -8, -8, 8, -8, -8, 8, 32, 32, 32, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32, 32, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -4, -4, -4, -4, 4, -4, 4, -4, -4, 4, 4, -4, -4, -4, 4, 4, -4, -4, 4, -4, -4, -4, -4, -16, -16, -16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -16, -16, -16, -16, -16, -16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348738
{'cdim': 40, 'counter': 33, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40a', 'multiplicity': 1, 'nt': [44, 87], 'qdim': 40, 'qvalues': [40, 40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, -4, 7, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, -4, 7, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348739
{'cdim': 40, 'counter': 34, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40b', 'multiplicity': 1, 'nt': [44, 87], 'qdim': 40, 'qvalues': [40, 40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 7, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 7, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 7, -4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, 7, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348740
{'cdim': 40, 'counter': 35, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40c', 'multiplicity': 1, 'nt': [44, 87], 'qdim': 40, 'qvalues': [40, 40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348741
{'cdim': 40, 'counter': 36, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40d', 'multiplicity': 1, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, 7, -4, 7, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 4, 4, -7, -7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348742
{'cdim': 40, 'counter': 37, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40e', 'multiplicity': 1, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 7, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -7, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, -4, -4, 7, -4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, -7, -7, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348743
{'cdim': 40, 'counter': 38, 'faithful': False, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40f', 'multiplicity': 1, 'nt': [88, 0], 'qdim': 40, 'qvalues': [40, -40, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -7, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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id: 4348744
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id: 4348746
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id: 4348747
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id: 4348748
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id: 4348749
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id: 4348750
{'cdim': 40, 'counter': 44, 'faithful': True, 'group': '29040.c', 'group_order': 29040, 'image': None, 'label': '29040.c.40l', 'multiplicity': 2, 'nt': [264, 0], 'qdim': 80, 'qvalues': [80, -80, 0, 0, -40, -40, 0, 0, 0, 0, 0, 0, 0, 0, 40, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, -8, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -14, 8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -7, -7, 4, 4, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, -4, -4, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
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gps_char • Show schema
Hide schema
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id: 6535932
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id: 6535948
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id: 6535958
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id: 6535959
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id: 6535960
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id: 6535961
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id: 6535962
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id: 6535963
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id: 6535964
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id: 6535949
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id: 6535950
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id: 6535951
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id: 6535952
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id: 6535953
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id: 6535954
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id: 6535956
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id: 6535957
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id: 6535965
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id: 6535975
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id: 6535976
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id: 6535978
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id: 6535979
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id: 6535980
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id: 6535981
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id: 6535982
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id: 6535967
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id: 6535968
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id: 6535969
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id: 6535970
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id: 6535971
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id: 6535972
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id: 6535973
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id: 6535974
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id: 6535983
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id: 6535993
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id: 6535994
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id: 6535995
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id: 6535996
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id: 6535997
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id: 6535998
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id: 6536000
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id: 6535984
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id: 6535985
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id: 6535986
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id: 6535987
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id: 6535989
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id: 6535990
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id: 6535991
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id: 6535992
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id: 6536001
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id: 6536011
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id: 6536012
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id: 6536013
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id: 6536014
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id: 6536015
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id: 6536016
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id: 6536017
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id: 6536002
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id: 6536003
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id: 6536004
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id: 6536005
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id: 6536006
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id: 6536007
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id: 6536008
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id: 6536009
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id: 6536018
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id: 6536028
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id: 6536029
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id: 6536030
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id: 6536031
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id: 6536033
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 29040, 'counter': 190, 'cyclotomic_n': 120, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '120.4', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 242, 'label': '29040.c.1ae14', 'nt': [120, 32], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 40]], [[-1, 20]], [[1, 30]], [[-1, 30]], [[-1, 30]], [[1, 30]], [[-1, 36]], [[1, 24]], [[-1, 12]], [[1, 48]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[-1, 20]], [[1, 40]], [[-1, 15]], [[1, 45]], [[1, 45]], [[-1, 15]], [[1, 15]], [[-1, 45]], [[-1, 45]], [[1, 15]], [[1, 12]], [[-1, 12]], [[-1, 48]], [[1, 24]], [[1, 48]], [[-1, 36]], [[-1, 48]], [[1, 36]], [[1, 36]], [[-1, 24]], [[1, 12]], [[-1, 24]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 10]], [[1, 50]], [[-1, 50]], [[1, 50]], [[1, 10]], [[-1, 10]], [[-1, 10]], [[-1, 50]], [[-1, 28]], [[1, 32]], [[-1, 44]], [[-1, 4]], [[1, 16]], [[-1, 52]], [[1, 56]], [[1, 8]], [[1, 54]], [[1, 54]], [[1, 6]], [[-1, 54]], [[-1, 42]], [[1, 42]], [[1, 42]], [[1, 18]], [[-1, 18]], [[-1, 42]], [[-1, 6]], [[-1, 6]], [[-1, 54]], [[1, 6]], [[-1, 18]], [[1, 18]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 55]], [[-1, 55]], [[-1, 35]], [[1, 55]], [[1, 35]], [[1, 5]], [[-1, 5]], [[1, 5]], [[-1, 25]], [[1, 25]], [[-1, 25]], [[1, 25]], [[-1, 5]], [[-1, 35]], [[-1, 55]], [[1, 35]], [[-1, 32]], [[1, 52]], [[1, 56]], [[-1, 28]], [[1, 4]], [[1, 28]], [[1, 8]], [[1, 52]], [[1, 16]], [[-1, 4]], [[1, 4]], [[-1, 8]], [[-1, 52]], [[-1, 16]], [[1, 28]], [[-1, 56]], [[-1, 16]], [[1, 32]], [[1, 44]], [[1, 44]], [[-1, 56]], [[-1, 32]], [[-1, 44]], [[-1, 8]], [[-1, 20]], [[1, 40]], [[-1, 20]], [[-1, 20]], [[1, 40]], [[1, 40]], [[-1, 33]], [[1, 51]], [[1, 51]], [[-1, 33]], [[-1, 21]], [[1, 27]], [[-1, 21]], [[1, 39]], [[1, 3]], [[-1, 9]], [[1, 27]], [[-1, 3]], [[1, 39]], [[-1, 27]], [[1, 21]], [[1, 57]], [[-1, 57]], [[-1, 39]], [[-1, 27]], [[-1, 39]], [[1, 9]], [[1, 9]], [[-1, 57]], [[-1, 9]], [[1, 57]], [[1, 21]], [[1, 3]], [[1, 33]], [[-1, 51]], [[-1, 3]], [[-1, 51]], [[1, 33]], [[-1, 58]], [[1, 22]], [[-1, 22]], [[-1, 34]], [[1, 38]], [[1, 34]], [[-1, 58]], [[1, 26]], [[1, 2]], [[1, 2]], [[1, 58]], [[1, 26]], [[1, 38]], [[-1, 26]], [[-1, 38]], [[1, 34]], [[1, 46]], [[-1, 2]], [[-1, 38]], [[-1, 14]], [[1, 58]], [[1, 22]], [[-1, 46]], [[-1, 22]], [[-1, 2]], [[-1, 46]], [[1, 46]], [[-1, 34]], [[-1, 14]], [[1, 14]], [[-1, 26]], [[1, 14]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[-1, 43]], [[1, 19]], [[1, 13]], [[-1, 41]], [[1, 47]], [[-1, 17]], [[-1, 47]], [[-1, 13]], [[-1, 19]], [[1, 49]], [[-1, 1]], [[-1, 7]], [[1, 43]], [[1, 17]], [[-1, 29]], [[1, 43]], [[1, 29]], [[1, 13]], [[-1, 23]], [[1, 41]], [[-1, 31]], [[1, 37]], [[-1, 43]], [[1, 7]], [[1, 1]], [[-1, 49]], [[-1, 37]], [[1, 31]], [[1, 31]], [[1, 17]], [[-1, 11]], [[1, 23]], [[1, 53]], [[1, 53]], [[-1, 47]], [[-1, 1]], [[1, 59]], [[-1, 49]], [[-1, 41]], [[-1, 7]], [[1, 29]], [[1, 19]], [[1, 37]], [[1, 11]], [[-1, 59]], [[1, 23]], [[-1, 13]], [[1, 59]], [[-1, 11]], [[-1, 37]], [[-1, 19]], [[-1, 29]], [[1, 7]], [[1, 41]], [[1, 49]], [[-1, 59]], [[1, 1]], [[1, 47]], [[-1, 53]], [[-1, 53]], [[-1, 23]], [[1, 11]], [[-1, 17]], [[-1, 31]]]}
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id: 6536034
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 29040, 'counter': 191, 'cyclotomic_n': 120, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '120.4', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 242, 'label': '29040.c.1ae15', 'nt': [120, 0], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 20]], [[1, 40]], [[-1, 30]], [[1, 30]], [[1, 30]], [[-1, 30]], [[1, 24]], [[-1, 36]], [[1, 48]], [[-1, 12]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[1, 40]], [[-1, 20]], [[-1, 45]], [[1, 15]], [[1, 15]], [[-1, 45]], [[1, 45]], [[-1, 15]], [[-1, 15]], [[1, 45]], [[-1, 48]], [[1, 48]], [[1, 12]], [[-1, 36]], [[-1, 12]], [[1, 24]], [[1, 12]], [[-1, 24]], [[-1, 24]], [[1, 36]], [[-1, 48]], [[1, 36]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 50]], [[-1, 10]], [[1, 10]], [[-1, 10]], [[-1, 50]], [[1, 50]], [[1, 50]], [[1, 10]], [[1, 32]], [[-1, 28]], [[1, 16]], [[1, 56]], [[-1, 44]], [[1, 8]], [[-1, 4]], [[-1, 52]], [[-1, 6]], [[-1, 6]], [[-1, 54]], [[1, 6]], [[1, 18]], [[-1, 18]], [[-1, 18]], [[-1, 42]], [[1, 42]], [[1, 18]], [[1, 54]], [[1, 54]], [[1, 6]], [[-1, 54]], [[1, 42]], [[-1, 42]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 5]], [[-1, 5]], [[-1, 25]], [[1, 5]], [[1, 25]], [[1, 55]], [[-1, 55]], [[1, 55]], [[-1, 35]], [[1, 35]], [[-1, 35]], [[1, 35]], [[-1, 55]], [[-1, 25]], [[-1, 5]], [[1, 25]], [[1, 28]], [[-1, 8]], [[-1, 4]], [[1, 32]], [[-1, 56]], [[-1, 32]], [[-1, 52]], [[-1, 8]], [[-1, 44]], [[1, 56]], [[-1, 56]], [[1, 52]], [[1, 8]], [[1, 44]], [[-1, 32]], [[1, 4]], [[1, 44]], [[-1, 28]], [[-1, 16]], [[-1, 16]], [[1, 4]], [[1, 28]], [[1, 16]], [[1, 52]], [[1, 40]], [[-1, 20]], [[1, 40]], [[1, 40]], [[-1, 20]], [[-1, 20]], [[-1, 27]], [[1, 9]], [[1, 9]], [[-1, 27]], [[-1, 39]], [[1, 33]], [[-1, 39]], [[1, 21]], [[1, 57]], [[-1, 51]], [[1, 33]], [[-1, 57]], [[1, 21]], [[-1, 33]], [[1, 39]], [[1, 3]], [[-1, 3]], [[-1, 21]], [[-1, 33]], [[-1, 21]], [[1, 51]], [[1, 51]], [[-1, 3]], [[-1, 51]], [[1, 3]], [[1, 39]], [[1, 57]], [[1, 27]], [[-1, 9]], [[-1, 57]], [[-1, 9]], [[1, 27]], [[1, 2]], [[-1, 38]], [[1, 38]], [[1, 26]], [[-1, 22]], [[-1, 26]], [[1, 2]], [[-1, 34]], [[-1, 58]], [[-1, 58]], [[-1, 2]], [[-1, 34]], [[-1, 22]], [[1, 34]], [[1, 22]], [[-1, 26]], [[-1, 14]], [[1, 58]], [[1, 22]], [[1, 46]], [[-1, 2]], [[-1, 38]], [[1, 14]], [[1, 38]], [[1, 58]], [[1, 14]], [[-1, 14]], [[1, 26]], [[1, 46]], [[-1, 46]], [[1, 34]], [[-1, 46]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 17]], [[1, 41]], [[1, 47]], [[-1, 19]], [[1, 13]], [[-1, 43]], [[-1, 13]], [[-1, 47]], [[-1, 41]], [[1, 11]], [[-1, 59]], [[-1, 53]], [[1, 17]], [[1, 43]], [[-1, 31]], [[1, 17]], [[1, 31]], [[1, 47]], [[-1, 37]], [[1, 19]], [[-1, 29]], [[1, 23]], [[-1, 17]], [[1, 53]], [[1, 59]], [[-1, 11]], [[-1, 23]], [[1, 29]], [[1, 29]], [[1, 43]], [[-1, 49]], [[1, 37]], [[1, 7]], [[1, 7]], [[-1, 13]], [[-1, 59]], [[1, 1]], [[-1, 11]], [[-1, 19]], [[-1, 53]], [[1, 31]], [[1, 41]], [[1, 23]], [[1, 49]], [[-1, 1]], [[1, 37]], [[-1, 47]], [[1, 1]], [[-1, 49]], [[-1, 23]], [[-1, 41]], [[-1, 31]], [[1, 53]], [[1, 19]], [[1, 11]], [[-1, 1]], [[1, 59]], [[1, 13]], [[-1, 7]], [[-1, 7]], [[-1, 37]], [[1, 49]], [[-1, 43]], [[-1, 29]]]}
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id: 6536035
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id: 6536036
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id: 6536037
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id: 6536038
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id: 6536019
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id: 6536039
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id: 6536040
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id: 6536041
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id: 6536042
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id: 6536045
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 29040, 'counter': 200, 'cyclotomic_n': 120, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '120.4', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 242, 'label': '29040.c.1ae24', 'nt': [120, 32], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 40]], [[-1, 20]], [[-1, 30]], [[1, 30]], [[1, 30]], [[-1, 30]], [[-1, 12]], [[1, 48]], [[1, 24]], [[-1, 36]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[-1, 20]], [[1, 40]], [[-1, 45]], [[1, 15]], [[1, 15]], [[-1, 45]], [[1, 45]], [[-1, 15]], [[-1, 15]], [[1, 45]], [[-1, 24]], [[1, 24]], [[1, 36]], [[1, 48]], [[-1, 36]], [[-1, 12]], [[1, 36]], [[1, 12]], [[1, 12]], [[-1, 48]], [[-1, 24]], [[-1, 48]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 10]], [[-1, 50]], [[1, 50]], [[-1, 50]], [[-1, 10]], [[1, 10]], [[1, 10]], [[1, 50]], [[1, 16]], [[-1, 44]], [[1, 8]], [[-1, 28]], [[-1, 52]], [[-1, 4]], [[1, 32]], [[1, 56]], [[1, 18]], [[1, 18]], [[1, 42]], [[-1, 18]], [[-1, 54]], [[1, 54]], [[1, 54]], [[1, 6]], [[-1, 6]], [[-1, 54]], [[-1, 42]], [[-1, 42]], [[-1, 18]], [[1, 42]], [[-1, 6]], [[1, 6]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 25]], [[1, 25]], [[1, 5]], [[-1, 25]], [[-1, 5]], [[-1, 35]], [[1, 35]], [[-1, 35]], [[1, 55]], [[-1, 55]], [[1, 55]], [[-1, 55]], [[1, 35]], [[1, 5]], [[1, 25]], [[-1, 5]], [[1, 44]], [[1, 4]], [[1, 32]], [[1, 16]], [[1, 28]], [[-1, 16]], [[1, 56]], [[1, 4]], [[-1, 52]], [[-1, 28]], [[1, 28]], [[-1, 56]], [[-1, 4]], [[1, 52]], [[-1, 16]], [[-1, 32]], [[1, 52]], [[-1, 44]], [[-1, 8]], [[-1, 8]], [[-1, 32]], [[1, 44]], [[1, 8]], [[-1, 56]], [[-1, 20]], [[1, 40]], [[-1, 20]], [[-1, 20]], [[1, 40]], [[1, 40]], [[-1, 51]], [[1, 57]], [[1, 57]], [[-1, 51]], [[1, 27]], [[1, 9]], [[1, 27]], [[-1, 33]], [[-1, 21]], [[-1, 3]], [[1, 9]], [[1, 21]], [[-1, 33]], [[-1, 9]], [[-1, 27]], [[-1, 39]], [[1, 39]], [[1, 33]], [[-1, 9]], [[1, 33]], [[1, 3]], [[1, 3]], [[1, 39]], [[-1, 3]], [[-1, 39]], [[-1, 27]], [[-1, 21]], [[1, 51]], [[-1, 57]], [[1, 21]], [[-1, 57]], [[1, 51]], [[-1, 46]], [[1, 34]], [[-1, 34]], [[1, 58]], [[1, 26]], [[-1, 58]], [[-1, 46]], [[-1, 2]], [[1, 14]], [[1, 14]], [[1, 46]], [[-1, 2]], [[1, 26]], [[1, 2]], [[-1, 26]], [[-1, 58]], [[-1, 22]], [[-1, 14]], [[-1, 26]], [[1, 38]], [[1, 46]], [[1, 34]], [[1, 22]], [[-1, 34]], [[-1, 14]], [[1, 22]], [[-1, 22]], [[1, 58]], [[1, 38]], [[-1, 38]], [[1, 2]], [[-1, 38]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[-1, 1]], [[-1, 13]], [[1, 31]], [[1, 47]], [[1, 29]], [[-1, 59]], [[-1, 29]], [[-1, 31]], [[1, 13]], [[1, 43]], [[1, 7]], [[1, 49]], [[1, 1]], [[1, 59]], [[-1, 23]], [[1, 1]], [[1, 23]], [[1, 31]], [[1, 41]], [[-1, 47]], [[-1, 37]], [[-1, 19]], [[-1, 1]], [[-1, 49]], [[-1, 7]], [[-1, 43]], [[1, 19]], [[1, 37]], [[1, 37]], [[1, 59]], [[-1, 17]], [[-1, 41]], [[-1, 11]], [[-1, 11]], [[-1, 29]], [[1, 7]], [[-1, 53]], [[-1, 43]], [[1, 47]], [[1, 49]], [[1, 23]], [[-1, 13]], [[-1, 19]], [[1, 17]], [[1, 53]], [[-1, 41]], [[-1, 31]], [[-1, 53]], [[-1, 17]], [[1, 19]], [[1, 13]], [[-1, 23]], [[-1, 49]], [[-1, 47]], [[1, 43]], [[1, 53]], [[-1, 7]], [[1, 29]], [[1, 11]], [[1, 11]], [[1, 41]], [[1, 17]], [[-1, 59]], [[-1, 37]]]}
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id: 6536046
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id: 6536047
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id: 6536048
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id: 6536049
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id: 6536050
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id: 6536020
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id: 6536051
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id: 6536052
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id: 6536053
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id: 6536022
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id: 6536023
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id: 6536024
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id: 6536025
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id: 6536026
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id: 6536027
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 29040, 'counter': 185, 'cyclotomic_n': 120, 'dim': 1, 'faithful': False, 'field': [1, 0, 0, 0, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '120.4', 'image_order': 120, 'indicator': 0, 'kernel': '120.b1.a1', 'kernel_order': 242, 'label': '29040.c.1ae9', 'nt': [120, 0], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 20]], [[1, 40]], [[-1, 30]], [[1, 30]], [[1, 30]], [[-1, 30]], [[-1, 36]], [[1, 24]], [[-1, 12]], [[1, 48]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[1, 40]], [[-1, 20]], [[1, 45]], [[-1, 15]], [[-1, 15]], [[1, 45]], [[-1, 45]], [[1, 15]], [[1, 15]], [[-1, 45]], [[1, 12]], [[-1, 12]], [[-1, 48]], [[1, 24]], [[1, 48]], [[-1, 36]], [[-1, 48]], [[1, 36]], [[1, 36]], [[-1, 24]], [[1, 12]], [[-1, 24]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 50]], [[-1, 10]], [[1, 10]], [[-1, 10]], [[-1, 50]], [[1, 50]], [[1, 50]], [[1, 10]], [[1, 8]], [[-1, 52]], [[-1, 4]], [[-1, 44]], [[1, 56]], [[1, 32]], [[1, 16]], [[-1, 28]], [[-1, 54]], [[-1, 54]], [[-1, 6]], [[1, 54]], [[1, 42]], [[-1, 42]], [[-1, 42]], [[-1, 18]], [[1, 18]], [[1, 42]], [[1, 6]], [[1, 6]], [[1, 54]], [[-1, 6]], [[1, 18]], [[-1, 18]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 5]], [[1, 5]], [[1, 25]], [[-1, 5]], [[-1, 25]], [[-1, 55]], [[1, 55]], [[-1, 55]], [[1, 35]], [[-1, 35]], [[1, 35]], [[-1, 35]], [[1, 55]], [[1, 25]], [[1, 5]], [[-1, 25]], [[1, 52]], [[-1, 32]], [[1, 16]], [[1, 8]], [[1, 44]], [[-1, 8]], [[-1, 28]], [[-1, 32]], [[1, 56]], [[-1, 44]], [[1, 44]], [[1, 28]], [[1, 32]], [[-1, 56]], [[-1, 8]], [[-1, 16]], [[-1, 56]], [[-1, 52]], [[1, 4]], [[1, 4]], [[-1, 16]], [[1, 52]], [[-1, 4]], [[1, 28]], [[1, 40]], [[-1, 20]], [[1, 40]], [[1, 40]], [[-1, 20]], [[-1, 20]], [[1, 3]], [[1, 21]], [[1, 21]], [[1, 3]], [[-1, 51]], [[-1, 57]], [[-1, 51]], [[1, 9]], [[-1, 33]], [[-1, 39]], [[-1, 57]], [[1, 33]], [[1, 9]], [[1, 57]], [[1, 51]], [[-1, 27]], [[1, 27]], [[-1, 9]], [[1, 57]], [[-1, 9]], [[1, 39]], [[1, 39]], [[1, 27]], [[-1, 39]], [[-1, 27]], [[1, 51]], [[-1, 33]], [[-1, 3]], [[-1, 21]], [[1, 33]], [[-1, 21]], [[-1, 3]], [[-1, 38]], [[1, 2]], [[-1, 2]], [[-1, 14]], [[1, 58]], [[1, 14]], [[-1, 38]], [[1, 46]], [[1, 22]], [[1, 22]], [[1, 38]], [[1, 46]], [[1, 58]], [[-1, 46]], [[-1, 58]], [[1, 14]], [[1, 26]], [[-1, 22]], [[-1, 58]], [[-1, 34]], [[1, 38]], [[1, 2]], [[-1, 26]], [[-1, 2]], [[-1, 22]], [[-1, 26]], [[1, 26]], [[-1, 14]], [[-1, 34]], [[1, 34]], [[-1, 46]], [[1, 34]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 40]], [[1, 20]], [[-1, 53]], [[1, 29]], [[-1, 23]], [[-1, 31]], [[-1, 37]], [[-1, 7]], [[1, 37]], [[1, 23]], [[-1, 29]], [[-1, 59]], [[1, 11]], [[-1, 17]], [[1, 53]], [[1, 7]], [[-1, 19]], [[1, 53]], [[1, 19]], [[-1, 23]], [[1, 13]], [[1, 31]], [[-1, 41]], [[-1, 47]], [[-1, 53]], [[1, 17]], [[-1, 11]], [[1, 59]], [[1, 47]], [[1, 41]], [[1, 41]], [[1, 7]], [[1, 1]], [[-1, 13]], [[1, 43]], [[1, 43]], [[1, 37]], [[1, 11]], [[-1, 49]], [[1, 59]], [[-1, 31]], [[-1, 17]], [[1, 19]], [[1, 29]], [[-1, 47]], [[-1, 1]], [[1, 49]], [[-1, 13]], [[1, 23]], [[-1, 49]], [[1, 1]], [[1, 47]], [[-1, 29]], [[-1, 19]], [[1, 17]], [[1, 31]], [[-1, 59]], [[1, 49]], [[-1, 11]], [[-1, 37]], [[-1, 43]], [[-1, 43]], [[1, 13]], [[-1, 1]], [[-1, 7]], [[-1, 41]]]}
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id: 6536054
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id: 6536064
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id: 6536065
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id: 6536067
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id: 6536068
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id: 6536069
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id: 6536070
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id: 6536071
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id: 6536072
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id: 6536073
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id: 6536074
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id: 6536056
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id: 6536075
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id: 6536076
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id: 6536078
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id: 6536079
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id: 6536080
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id: 6536081
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id: 6536082
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id: 6536083
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id: 6536084
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id: 6536085
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id: 6536057
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id: 6536086
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id: 6536087
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id: 6536089
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id: 6536058
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id: 6536059
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id: 6536060
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id: 6536061
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id: 6536062
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id: 6536063
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id: 6536043
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id: 6536113
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id: 6536124
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id: 6536135
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id: 6536146
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id: 6536157
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id: 6536168
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id: 6536179
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id: 6535933
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id: 6535944
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id: 6535955
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id: 6535966
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id: 6535977
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id: 6535988
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id: 6535999
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id: 6536010
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id: 6536021
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id: 6536032
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id: 6536044
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id: 6536055
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id: 6536066
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id: 6536077
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id: 6536088
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id: 6536099
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id: 6536109
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id: 6536110
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id: 6536111
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id: 6536112
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id: 6536114
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id: 6536115
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id: 6536116
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id: 6536117
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id: 6536118
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id: 6536119
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id: 6536120
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id: 6536121
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id: 6536122
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id: 6536123
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id: 6536125
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id: 6536126
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id: 6536127
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id: 6536128
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id: 6536129
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id: 6536130
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id: 6536131
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id: 6536132
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id: 6536133
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id: 6536134
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id: 6536136
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id: 6536137
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id: 6536138
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id: 6536139
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id: 6536140
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id: 6536141
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id: 6536142
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id: 6536143
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id: 6536144
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id: 6536145
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id: 6536147
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id: 6536148
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id: 6536149
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id: 6536150
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id: 6536151
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id: 6536152
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id: 6536153
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id: 6536154
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id: 6536155
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id: 6536156
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id: 6536158
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id: 6536159
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id: 6536160
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id: 6536161
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id: 6536162
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id: 6536163
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id: 6536164
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id: 6536165
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id: 6536166
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id: 6536167
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id: 6536169
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id: 6536170
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id: 6536171
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id: 6536172
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id: 6536173
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id: 6536174
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id: 6536175
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id: 6536176
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id: 6536177
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id: 6536178
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id: 6536180
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id: 6536181
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id: 6536182
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id: 6536183
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id: 6536184
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id: 6536185
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id: 6536186
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id: 6536187
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id: 6536188
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id: 6536189
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id: 6535934
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id: 6535935
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id: 6535936
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id: 6535937
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id: 6535938
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id: 6535939
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id: 6535940
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id: 6535941
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id: 6535942
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id: 6535943
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 29040, 'counter': 109, 'cyclotomic_n': 15, 'dim': 1, 'faithful': False, 'field': [1, -1, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '30.4', 'image_order': 30, 'indicator': 0, 'kernel': '30.a1.a1', 'kernel_order': 968, 'label': '29040.c.1z5', 'nt': [30, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -5]], [[1, 5]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -3]], [[1, 3]], [[1, -6]], [[1, 6]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, -5]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, -6]], [[1, -6]], [[1, 6]], [[1, 3]], [[1, 6]], [[1, -3]], [[1, 6]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -6]], [[1, 3]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, -5]], [[1, 5]], [[1, 5]], [[1, 5]], [[1, -5]], [[1, -5]], [[1, -5]], [[1, 5]], [[1, 1]], [[1, -1]], [[1, -7]], [[1, -2]], [[1, 7]], [[1, 4]], [[1, 2]], [[1, -4]], [[1, 3]], [[1, 3]], [[1, -3]], [[1, 3]], [[1, -6]], [[1, -6]], [[1, -6]], [[1, 6]], [[1, 6]], [[1, -6]], [[1, -3]], [[1, -3]], [[1, 3]], [[1, -3]], [[1, 6]], [[1, 6]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, -5]], [[-1, -5]], [[-1, 5]], [[-1, -5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, 5]], [[-1, -5]], [[-1, -5]], [[-1, -5]], [[-1, -5]], [[-1, 5]], [[-1, 5]], [[-1, -5]], [[-1, 5]], [[1, -1]], [[1, 4]], [[1, 2]], [[1, 1]], [[1, -2]], [[1, 1]], [[1, -4]], [[1, 4]], [[1, 7]], [[1, -2]], [[1, -2]], [[1, -4]], [[1, 4]], [[1, 7]], [[1, 1]], [[1, 2]], [[1, 7]], [[1, -1]], [[1, -7]], [[1, -7]], [[1, 2]], [[1, -1]], [[1, -7]], [[1, -4]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, 5]], [[1, -5]], [[1, -5]], [[-1, 6]], [[-1, -3]], [[-1, -3]], [[-1, 6]], [[-1, -3]], [[-1, -6]], [[-1, -3]], [[-1, 3]], [[-1, 6]], [[-1, 3]], [[-1, -6]], [[-1, 6]], [[-1, 3]], [[-1, -6]], [[-1, -3]], [[-1, -6]], [[-1, -6]], [[-1, 3]], [[-1, -6]], [[-1, 3]], [[-1, 3]], [[-1, 3]], [[-1, -6]], [[-1, 3]], [[-1, -6]], [[-1, -3]], [[-1, 6]], [[-1, 6]], [[-1, -3]], [[-1, 6]], [[-1, -3]], [[-1, 6]], [[1, 1]], [[1, 4]], [[1, 4]], [[1, -2]], [[1, -4]], [[1, -2]], [[1, 1]], [[1, 2]], [[1, -1]], [[1, -1]], [[1, 1]], [[1, 2]], [[1, -4]], [[1, 2]], [[1, -4]], [[1, -2]], [[1, 7]], [[1, -1]], [[1, -4]], [[1, -7]], [[1, 1]], [[1, 4]], [[1, 7]], [[1, 4]], [[1, -1]], [[1, 7]], [[1, 7]], [[1, -2]], [[1, -7]], [[1, -7]], [[1, 2]], [[1, -7]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, -5]], [[1, 5]], [[1, -5]], [[-1, 1]], [[-1, -2]], [[-1, 1]], [[-1, 2]], [[-1, -1]], [[-1, -1]], [[-1, -1]], [[-1, 1]], [[-1, -2]], [[-1, -2]], [[-1, 7]], [[-1, 4]], [[-1, 1]], [[-1, -1]], [[-1, -7]], [[-1, 1]], [[-1, -7]], [[-1, 1]], [[-1, -4]], [[-1, 2]], [[-1, 7]], [[-1, 4]], [[-1, 1]], [[-1, 4]], [[-1, 7]], [[-1, -2]], [[-1, 4]], [[-1, 7]], [[-1, 7]], [[-1, -1]], [[-1, 2]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, -1]], [[-1, 7]], [[-1, -7]], [[-1, -2]], [[-1, 2]], [[-1, 4]], [[-1, -7]], [[-1, -2]], [[-1, 4]], [[-1, 2]], [[-1, -7]], [[-1, -4]], [[-1, 1]], [[-1, -7]], [[-1, 2]], [[-1, 4]], [[-1, -2]], [[-1, -7]], [[-1, 4]], [[-1, 2]], [[-1, -2]], [[-1, -7]], [[-1, 7]], [[-1, -1]], [[-1, -4]], [[-1, -4]], [[-1, -4]], [[-1, 2]], [[-1, -1]], [[-1, 7]]]}
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id: 6535945
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id: 6535946
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id: 6535947
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id: 6536090
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id: 6536091
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id: 6536092
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id: 6536093
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id: 6536094
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id: 6536095
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id: 6536096
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id: 6536097
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id: 6536098
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id: 6536100
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id: 6536101
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id: 6536102
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id: 6536103
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id: 6536104
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id: 6536105
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id: 6536106
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id: 6536107
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id: 6536108
{'center': '4840.a1.a1', 'center_index': 4840, 'center_order': 6, 'counter': 258, 'cyclotomic_n': 3, 'dim': 40, 'faithful': True, 'field': [1, -1, 1], 'group': '29040.c', 'group_counter': 3, 'group_order': 29040, 'image': None, 'image_isoclass': '29040.c', 'image_order': 29040, 'indicator': 0, 'kernel': '29040.a1.a1', 'kernel_order': 1, 'label': '29040.c.40l2', 'nt': [264, 2], 'q_character': None, 'values': [[[40, 0]], [[-40, 0]], [[0, 0]], [[0, 0]], [[40, 1]], [[40, -1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-40, -1]], [[-40, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[7, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, 0]], [[4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[7, -1]], [[7, 1]], [[-4, -1]], [[-4, -1]], [[-4, 1]], [[-4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-7, -1]], [[-7, 1]], [[4, -1]], [[4, 1]], [[4, -1]], [[4, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 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: 65028397
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 29040, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 330, 'label': '29040.c.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, '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': '29040.c', 'subgroup_hash': 1832492014362143934, 'subgroup_order': 29040, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{120}', 'supersolvable': False, 'sylow': 0}
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id: 65028457
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 14520, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '14520.h', 'subgroup_hash': 5713675037625723248, 'subgroup_order': 14520, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{60}', 'supersolvable': False, 'sylow': 0}
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id: 65028468
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 14520, 'counter': 3, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '29040.c.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '14520.d', 'subgroup_hash': 4529086272714682210, 'subgroup_order': 14520, 'subgroup_tex': 'C_{11}^2:C_{120}', 'supersolvable': False, 'sylow': 0}
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id: 65028479
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 14520, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '29040.c.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, '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': '14520.d', 'subgroup_hash': 4529086272714682210, 'subgroup_order': 14520, 'subgroup_tex': 'C_{11}^2:C_{120}', 'supersolvable': False, 'sylow': 0}
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id: 65028490
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': True, 'core_order': 9680, 'counter': 5, 'cyclic': False, 'direct': True, 'hall': 110, 'label': '29040.c.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '9680.a', 'subgroup_hash': 3020249352014106621, 'subgroup_order': 9680, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{40}', 'supersolvable': False, 'sylow': 0}
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id: 65028501
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 7260, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '7260.e', 'subgroup_hash': 95388639074804745, 'subgroup_order': 7260, 'subgroup_tex': 'C_{66}:F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 65028512
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 7260, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.4.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '7260.f', 'subgroup_hash': 7584372576544646636, 'subgroup_order': 7260, 'subgroup_tex': 'C_{11}^2:C_{60}', 'supersolvable': False, 'sylow': 0}
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id: 65028523
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 7260, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.4.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1.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': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '7260.f', 'subgroup_hash': 7584372576544646636, 'subgroup_order': 7260, 'subgroup_tex': 'C_{11}^2:C_{60}', 'supersolvable': False, 'sylow': 0}
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id: 65028534
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 5808, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 66, 'label': '29040.c.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5808.b', 'subgroup_hash': 5432034713784547124, 'subgroup_order': 5808, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{24}', 'supersolvable': False, 'sylow': 0}
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id: 65028398
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 4840, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4840.a', 'subgroup_hash': 7121737719162348494, 'subgroup_order': 4840, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{20}', 'supersolvable': False, 'sylow': 0}
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id: 65028409
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4840, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '29040.c.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4840.c', 'subgroup_hash': 1340125317553616686, 'subgroup_order': 4840, 'subgroup_tex': 'C_{11}^2:C_{40}', 'supersolvable': False, 'sylow': 0}
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id: 65028420
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': True, 'centralizer_order': 6, 'characteristic': False, 'core_order': 4840, 'counter': 12, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '29040.c.6.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '6.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4840.c', 'subgroup_hash': 1340125317553616686, 'subgroup_order': 4840, 'subgroup_tex': 'C_{11}^2:C_{40}', 'supersolvable': False, 'sylow': 0}
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id: 65028431
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 3630, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3630.c', 'subgroup_hash': 5479765184792582402, 'subgroup_order': 3630, 'subgroup_tex': 'C_{11}^2:C_{30}', 'supersolvable': True, 'sylow': 0}
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id: 65028442
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 3630, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3630.d', 'subgroup_hash': 1613816561754299673, 'subgroup_order': 3630, 'subgroup_tex': 'C_{33}:F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 65028452
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 3630, 'counter': 15, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '8.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3630.d', 'subgroup_hash': 1613816561754299673, 'subgroup_order': 3630, 'subgroup_tex': 'C_{33}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028453
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2904, 'counter': 16, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.10.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2904.i', 'subgroup_hash': 436174279797151299, 'subgroup_order': 2904, 'subgroup_tex': 'C_2\\times C_{11}^2:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 65028454
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2904, 'counter': 17, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.10.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2904.e', 'subgroup_hash': 1798533995276121009, 'subgroup_order': 2904, 'subgroup_tex': 'C_{11}^2:C_{24}', 'supersolvable': False, 'sylow': 0}
-
id: 65028455
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2904, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.10.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '2904.e', 'subgroup_hash': 1798533995276121009, 'subgroup_order': 2904, 'subgroup_tex': 'C_{11}^2:C_{24}', 'supersolvable': False, 'sylow': 0}
-
id: 65028456
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2420, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2420.c', 'subgroup_hash': 6641519007809634494, 'subgroup_order': 2420, 'subgroup_tex': 'C_{22}:F_{11}', 'supersolvable': True, 'sylow': 0}
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id: 65028458
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2420, 'counter': 20, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2420.b', 'subgroup_hash': 4831136090400852969, 'subgroup_order': 2420, 'subgroup_tex': 'C_{11}^2:C_{20}', 'supersolvable': False, 'sylow': 0}
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id: 65028459
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 2420, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2420.b', 'subgroup_hash': 4831136090400852969, 'subgroup_order': 2420, 'subgroup_tex': 'C_{11}^2:C_{20}', 'supersolvable': False, 'sylow': 0}
-
id: 65028460
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1936, 'counter': 22, 'cyclic': False, 'direct': False, 'hall': 22, 'label': '29040.c.15.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '15.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '15.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 15, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{15}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1936.160', 'subgroup_hash': 160, 'subgroup_order': 1936, 'subgroup_tex': 'C_2\\times C_{11}^2:C_8', 'supersolvable': False, 'sylow': 0}
-
id: 65028461
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1815, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 165, 'label': '29040.c.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '16.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1815.5', 'subgroup_hash': 5, 'subgroup_order': 1815, 'subgroup_tex': 'C_{11}^2:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 65028462
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1452, 'counter': 24, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.20.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1452.36', 'subgroup_hash': 36, 'subgroup_order': 1452, 'subgroup_tex': 'C_{33}:D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028463
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1452, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.20.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1452.25', 'subgroup_hash': 25, 'subgroup_order': 1452, 'subgroup_tex': 'C_{11}^2:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 65028464
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1452, 'counter': 26, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.20.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1452.25', 'subgroup_hash': 25, 'subgroup_order': 1452, 'subgroup_tex': 'C_{11}^2:C_{12}', 'supersolvable': False, 'sylow': 0}
-
id: 65028465
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1210, 'counter': 27, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.19', 'subgroup_hash': 19, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}^2:C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028466
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1210, 'counter': 28, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{24}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028467
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 1210, 'counter': 29, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '1210.9', 'subgroup_hash': 9, 'subgroup_order': 1210, 'subgroup_tex': 'C_{11}:F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028469
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 968, 'counter': 30, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.30.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '30.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '968.38', 'subgroup_hash': 38, 'subgroup_order': 968, 'subgroup_tex': 'C_2\\times C_{11}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 65028470
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 968, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.30.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '30.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '968.35', 'subgroup_hash': 35, 'subgroup_order': 968, 'subgroup_tex': 'C_{11}^2:C_8', 'supersolvable': False, 'sylow': 0}
-
id: 65028471
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 968, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.30.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '30.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '30.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 30, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{30}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '968.35', 'subgroup_hash': 35, 'subgroup_order': 968, 'subgroup_tex': 'C_{11}^2:C_8', 'supersolvable': False, 'sylow': 0}
-
id: 65028472
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': True, 'core_order': 726, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.40.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '40.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}', 'simple': False, 'solvable': True, 'special_labels': ['F', 'S'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '726.13', 'subgroup_hash': 13, 'subgroup_order': 726, 'subgroup_tex': 'C_{11}\\times C_{66}', 'supersolvable': True, 'sylow': 0}
-
id: 65028473
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 726, 'counter': 34, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.40.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '726.9', 'subgroup_hash': 9, 'subgroup_order': 726, 'subgroup_tex': 'C_{33}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028474
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 726, 'counter': 35, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.40.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '40.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '40.9', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 9, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 40, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{20}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '726.9', 'subgroup_hash': 9, 'subgroup_order': 726, 'subgroup_tex': 'C_{33}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028475
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.44.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '660.17', 'subgroup_hash': 17, 'subgroup_order': 660, 'subgroup_tex': 'C_6\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028476
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.44.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '660.17', 'subgroup_hash': 17, 'subgroup_order': 660, 'subgroup_tex': 'C_6\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028477
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.44.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '44.a1.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': 44, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '660.17', 'subgroup_hash': 17, 'subgroup_order': 660, 'subgroup_tex': 'C_6\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028478
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 605, 'counter': 39, 'cyclic': False, 'direct': False, 'hall': 55, 'label': '29040.c.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.23', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{24}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '605.4', 'subgroup_hash': 4, 'subgroup_order': 605, 'subgroup_tex': 'C_{11}^2:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 65028480
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 484, 'counter': 40, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.60.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{60}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '484.11', 'subgroup_hash': 11, 'subgroup_order': 484, 'subgroup_tex': 'C_{11}:D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028481
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 484, 'counter': 41, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.60.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{60}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '484.8', 'subgroup_hash': 8, 'subgroup_order': 484, 'subgroup_tex': 'C_{11}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 65028482
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 484, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.60.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '60.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '60.13', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 60, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{30}', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '484.8', 'subgroup_hash': 8, 'subgroup_order': 484, 'subgroup_tex': 'C_{11}^2:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 65028483
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': True, 'core_order': 363, 'counter': 43, 'cyclic': False, 'direct': False, 'hall': 33, 'label': '29040.c.80.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '80.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '80.23', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 23, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 80, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{40}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '363.3', 'subgroup_hash': 3, 'subgroup_order': 363, 'subgroup_tex': 'C_{11}\\times C_{33}', 'supersolvable': True, 'sylow': 0}
-
id: 65028484
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.4', 'subgroup_hash': 4, 'subgroup_order': 330, 'subgroup_tex': 'C_{11}:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028485
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.4', 'subgroup_hash': 4, 'subgroup_order': 330, 'subgroup_tex': 'C_{11}:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028486
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.a1.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.4', 'subgroup_hash': 4, 'subgroup_order': 330, 'subgroup_tex': 'C_{11}:C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028487
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028488
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028489
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.b1.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028491
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028492
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028493
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.88.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '88.c1.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': 88, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '330.1', 'subgroup_hash': 1, 'subgroup_order': 330, 'subgroup_tex': 'C_3\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028494
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': True, 'core_order': 242, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.120.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '120.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{120}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.5', 'subgroup_hash': 5, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}\\times C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028495
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 242, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.120.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{120}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028496
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 242, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '29040.c.120.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '120.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '120.31', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 31, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 120, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{60}', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '242.4', 'subgroup_hash': 4, 'subgroup_order': 242, 'subgroup_tex': 'C_{11}:D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028497
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 30, 'label': '29040.c.121.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '121.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': 121, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '240.84', 'subgroup_hash': 84, 'subgroup_order': 240, 'subgroup_tex': 'C_2\\times C_{120}', 'supersolvable': True, 'sylow': 0}
-
id: 65028498
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.132.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028499
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.132.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028500
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.132.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '132.a1.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': 132, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028502
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.176.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 65028503
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.176.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '176.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': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 65028504
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.176.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '176.a1.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': 176, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '165.1', 'subgroup_hash': 1, 'subgroup_order': 165, 'subgroup_tex': 'C_{11}:C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 65028505
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.220.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028506
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.220.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028507
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 6, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.220.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '220.a1.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': 220, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '132.7', 'subgroup_hash': 7, 'subgroup_order': 132, 'subgroup_tex': 'C_3\\times D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028508
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': True, 'core_order': 121, 'counter': 66, 'cyclic': False, 'direct': False, 'hall': 11, 'label': '29040.c.240.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '240.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '240.84', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 84, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 240, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{120}', 'simple': False, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '121.2', 'subgroup_hash': 2, 'subgroup_order': 121, 'subgroup_tex': 'C_{11}^2', 'supersolvable': True, 'sylow': 11}
-
id: 65028509
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.242.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
-
id: 65028510
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 68, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.242.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.4', 'subgroup_hash': 4, 'subgroup_order': 120, 'subgroup_tex': 'C_{120}', 'supersolvable': True, 'sylow': 0}
-
id: 65028511
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 69, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.242.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '242.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': 242, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '120.4', 'subgroup_hash': 4, 'subgroup_order': 120, 'subgroup_tex': 'C_{120}', 'supersolvable': True, 'sylow': 0}
-
id: 65028513
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028514
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028515
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.a1.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.2', 'subgroup_hash': 2, 'subgroup_order': 110, 'subgroup_tex': 'C_{11}:C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028516
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028517
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028518
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.b1.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028519
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028520
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028521
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.264.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '264.c1.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': 264, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028522
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 10, 'label': '29040.c.363.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '363.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': 363, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '80.23', 'subgroup_hash': 23, 'subgroup_order': 80, 'subgroup_tex': 'C_2\\times C_{40}', 'supersolvable': True, 'sylow': 0}
-
id: 65028524
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 6, 'counter': 80, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.440.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
-
id: 65028525
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 6, 'counter': 81, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.440.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
-
id: 65028526
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 6, 'counter': 82, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.440.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '440.a1.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': 4, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
-
id: 65028527
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028528
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028529
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.b1.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028530
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028531
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028532
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 3, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.440.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '440.c1.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': 440, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.2', 'subgroup_hash': 2, 'subgroup_order': 66, 'subgroup_tex': 'C_3\\times D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028533
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.484.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '484.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': 484, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.13', 'subgroup_hash': 13, 'subgroup_order': 60, 'subgroup_tex': 'C_2\\times C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028535
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 90, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.484.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '484.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': 484, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
-
id: 65028536
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 91, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.484.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '484.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': 484, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '60.4', 'subgroup_hash': 4, 'subgroup_order': 60, 'subgroup_tex': 'C_{60}', 'supersolvable': True, 'sylow': 0}
-
id: 65028537
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.528.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 65028538
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.528.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '528.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
-
id: 65028539
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.528.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '528.a1.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': 528, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '55.1', 'subgroup_hash': 1, 'subgroup_order': 55, 'subgroup_tex': 'C_{11}:C_5', 'supersolvable': True, 'sylow': 0}
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id: 65028540
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 6, 'label': '29040.c.605.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '605.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': 605, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.23', 'subgroup_hash': 23, 'subgroup_order': 48, 'subgroup_tex': 'C_2\\times C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 65028541
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.660.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
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id: 65028542
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.660.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.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': 660, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028543
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.660.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '660.a1.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': 660, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '44.3', 'subgroup_hash': 3, 'subgroup_order': 44, 'subgroup_tex': 'D_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028544
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.726.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '726.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': 726, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.9', 'subgroup_hash': 9, 'subgroup_order': 40, 'subgroup_tex': 'C_2\\times C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 65028399
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 100, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.726.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '726.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': 726, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
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id: 65028400
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 101, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.726.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '726.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': 726, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '40.2', 'subgroup_hash': 2, 'subgroup_order': 40, 'subgroup_tex': 'C_{40}', 'supersolvable': True, 'sylow': 0}
-
id: 65028401
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 3, 'counter': 102, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.880.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '880.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': 880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
-
id: 65028402
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 3, 'counter': 103, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.880.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '880.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': 880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
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id: 65028403
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 3, 'counter': 104, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.880.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '880.a1.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': 880, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '33.1', 'subgroup_hash': 1, 'subgroup_order': 33, 'subgroup_tex': 'C_{33}', 'supersolvable': True, 'sylow': 0}
-
id: 65028404
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 105, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.968.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '968.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': 968, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028405
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 106, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.968.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '968.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': 968, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028406
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 107, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.968.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '968.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': 968, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '30.4', 'subgroup_hash': 4, 'subgroup_order': 30, 'subgroup_tex': 'C_{30}', 'supersolvable': True, 'sylow': 0}
-
id: 65028407
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1210.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.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': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 65028408
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 109, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1210.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.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': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 65028410
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 110, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1210.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1210.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': 1210, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.2', 'subgroup_hash': 2, 'subgroup_order': 24, 'subgroup_tex': 'C_{24}', 'supersolvable': True, 'sylow': 0}
-
id: 65028411
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1320.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028412
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1320.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028413
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1320.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1320.a1.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.2', 'subgroup_hash': 2, 'subgroup_order': 22, 'subgroup_tex': 'C_{22}', 'supersolvable': True, 'sylow': 0}
-
id: 65028414
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028415
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028416
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.b1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.b1.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028417
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 117, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028418
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 118, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028419
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 119, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1320.c1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '1320.c1.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': 1320, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '22.1', 'subgroup_hash': 1, 'subgroup_order': 22, 'subgroup_tex': 'D_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028421
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.1452.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1452.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': 1452, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.5', 'subgroup_hash': 5, 'subgroup_order': 20, 'subgroup_tex': 'C_2\\times C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028422
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 121, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1452.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1452.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': 1452, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 65028423
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 122, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.1452.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1452.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': 1452, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '20.2', 'subgroup_hash': 2, 'subgroup_order': 20, 'subgroup_tex': 'C_{20}', 'supersolvable': True, 'sylow': 0}
-
id: 65028424
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '29040.c.1815.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1815.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': 1815, 'quotient_simple': 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': 2}
-
id: 65028425
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 124, 'cyclic': True, 'direct': None, 'hall': 15, 'label': '29040.c.1936.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '1936.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': 1936, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15.1', 'subgroup_hash': 1, 'subgroup_order': 15, 'subgroup_tex': 'C_{15}', 'supersolvable': True, 'sylow': 0}
-
id: 65028426
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 6, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.2420.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2420.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': 2420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.5', 'subgroup_hash': 5, 'subgroup_order': 12, 'subgroup_tex': 'C_2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 65028427
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 126, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2420.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2420.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': 2420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 65028428
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 127, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2420.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2420.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': 2420, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 65028429
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 1, 'counter': 128, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2640.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2640.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': 2640, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028430
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 1, 'counter': 129, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2640.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2640.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': 2640, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028432
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 726, 'characteristic': False, 'core_order': 1, 'counter': 130, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2640.a1.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2640.a1.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': 2640, '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': '11.1', 'subgroup_hash': 1, 'subgroup_order': 11, 'subgroup_tex': 'C_{11}', 'supersolvable': True, 'sylow': 0}
-
id: 65028433
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2904.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2904.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': 2904, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028434
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 132, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2904.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2904.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': 2904, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028435
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 133, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.2904.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '2904.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': 2904, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '10.2', 'subgroup_hash': 2, 'subgroup_order': 10, 'subgroup_tex': 'C_{10}', 'supersolvable': True, 'sylow': 0}
-
id: 65028436
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.3630.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3630.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': 3630, 'quotient_simple': 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}
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id: 65028437
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 135, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.3630.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3630.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': 3630, 'quotient_simple': 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: 65028438
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 136, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.3630.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3630.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': 3630, 'quotient_simple': 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: 65028439
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': True, 'central_factor': False, 'centralizer_order': 29040, 'characteristic': True, 'core_order': 6, 'counter': 137, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '29040.c.4840.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4840.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4840.c', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1340125317553616686, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 4840, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{11}^2:C_{40}', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 65028440
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 138, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.4840.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4840.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': 4840, 'quotient_simple': 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: 65028441
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 3, 'counter': 139, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.4840.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '4840.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': 4840, 'quotient_simple': 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: 65028443
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 140, 'cyclic': True, 'direct': None, 'hall': 5, 'label': '29040.c.5808.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '5808.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': 5808, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
-
id: 65028444
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 2, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '29040.c.7260.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7260.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': 7260, 'quotient_simple': 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: 65028445
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 142, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.7260.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7260.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': 7260, 'quotient_simple': 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: 65028446
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 143, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.7260.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '7260.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': 7260, 'quotient_simple': 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: 65028447
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': True, 'central_factor': False, 'centralizer_order': 29040, 'characteristic': True, 'core_order': 3, 'counter': 144, 'cyclic': True, 'direct': True, 'hall': 3, 'label': '29040.c.9680.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '9680.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '9680.a', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3020249352014106621, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 9680, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_{11}^2:C_{40}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
-
id: 65028448
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': True, 'central_factor': False, 'centralizer_order': 29040, 'characteristic': True, 'core_order': 2, 'counter': 145, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '29040.c.14520.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '14520.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '14520.d', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4529086272714682210, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 14520, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_{11}^2:C_{120}', 'simple': True, 'solvable': True, 'special_labels': [], '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: 65028449
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.14520.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14520.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': 14520, '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: 65028450
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '29040.c.14520.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '14520.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': 14520, '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: 65028451
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '29040.c', 'ambient_counter': 3, 'ambient_order': 29040, 'ambient_tex': 'C_2\\times C_{11}^2:C_{120}', 'central': True, 'central_factor': False, 'centralizer_order': 29040, 'characteristic': True, 'core_order': 1, 'counter': 148, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '29040.c.29040.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '29040.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '29040.c', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1832492014362143934, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 29040, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times C_{11}^2:C_{120}', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'PC', 'U1', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
Hide schema
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id: 65028397
{'ambient': '29040.c', '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': '4840.a1.a1', 'complements': ['29040.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '3.a1.a1', '5.a1.a1', '121.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [969, 8236, 846, 8095, 8534, 7552, 8643, 6817], 'generators': [15, 30, 18600, 80, 60, 2640, 14520, 24], 'label': '29040.c.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', '3.a1.a1', '5.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '4840.c', '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': '4840.c'}
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id: 65028398
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '6.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.b1.a1', '12.c1.a1', '30.a1.a1', '726.a1.a1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3759, 6653, 2178, 5195, 6220, 7150, 7029, 5972], 'generators': [14520, 2640, 24, 60, 30, 2760], 'label': '29040.c.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1', '3.a1.a1'], 'normal_contains': ['12.a1.a1', '12.c1.a1', '12.b1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
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id: 65028399
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '726.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '242.b1.a1', '363.a1.a1'], 'contains': ['1452.c1.a1', '3630.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1119, -1, 1126, -1, 8899, -1, 9063, -1], 'generators': [15, 30, 60, 24], 'label': '29040.c.726.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '726.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '726.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028400
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '726.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '242.b1.b1', '363.a1.a1'], 'contains': ['1452.c1.a1', '3630.b1.b1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1119, -1, 703, -1, 8899, -1, 8724, -1], 'generators': [14535, 30, 60, 24], 'label': '29040.c.726.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '726.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '726.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028401
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '176.a1.a1', '440.a1.a1', '440.b1.a1', '440.c1.a1'], 'contains': ['2640.a1.a1', '9680.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8116, -1, 7743, -1, 3836, -1, 3822, -1], 'generators': [80, 2640], 'label': '29040.c.880.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '880.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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id: 65028402
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '176.a1.b1', '440.a1.b1', '440.b1.b1', '440.c1.b1'], 'contains': ['2640.a1.b1', '9680.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8116, -1, 6169, -1, 3836, -1, 3682, -1], 'generators': [80, 2760], 'label': '29040.c.880.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '880.a1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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id: 65028403
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '880.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['80.a1.a1', '176.a1.c1', '440.a1.c1', '440.b1.c1', '440.c1.c1'], 'contains': ['2640.a1.c1', '9680.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [8116, -1, 7440, -1, 3836, -1, 3542, -1], 'generators': [80, 21240], 'label': '29040.c.880.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '880.a1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '880.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
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id: 65028404
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '968.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['88.a1.a1', '88.a1.b1', '88.a1.c1', '484.a1.a1'], 'contains': ['1936.a1.a1', '2904.a1.a1', '4840.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6668, -1, 9091, -1, 4568, -1, 56, -1], 'generators': [14520, 24, 80], 'label': '29040.c.968.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '968.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '968.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028405
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '968.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['88.b1.a1', '88.b1.b1', '88.b1.c1', '484.a1.a1'], 'contains': ['1936.a1.a1', '2904.b1.a1', '4840.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [9234, -1, 7009, -1, 5735, -1, 2264, -1], 'generators': [14580, 24, 80], 'label': '29040.c.968.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '968.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '968.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028406
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '968.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['88.c1.a1', '88.c1.b1', '88.c1.c1', '484.a1.a1', '484.b1.a1', '484.c1.a1'], 'contains': ['1936.a1.a1', '2904.c1.a1', '4840.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4675, -1, 3884, -1, 6666, -1, 6071, -1], 'generators': [60, 24, 80], 'label': '29040.c.968.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '968.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '968.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028407
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1210.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.a1.a1', '242.a1.a1', '605.a1.a1'], 'contains': ['2420.a1.a1', '2420.b1.a1', '2420.c1.a1', '3630.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2649, -1, 1407, -1, 8385, -1, 8122, -1], 'generators': [14520, 30, 80, 60], 'label': '29040.c.1210.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028408
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1210.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.a1', '242.b1.a1', '605.a1.a1'], 'contains': ['2420.c1.a1', '3630.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [789, -1, 875, -1, 9528, -1, 9418, -1], 'generators': [15, 80, 30, 60], 'label': '29040.c.1210.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028409
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['4840.a1.a1', '4840.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '3.a1.a1'], 'contains': ['12.c1.a1', '30.b1.a1', '726.b1.a1'], 'core': '6.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1733, 9499, 1315, 8437, 7987, 9701, 9138, 9725], 'generators': [15, 2640, 30, 60, 24, 18600], 'label': '29040.c.6.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.a1', 'normal_contained_in': ['2.b1.a1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '30.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
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id: 65028410
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1210.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['10.b1.b1', '242.b1.b1', '605.a1.a1'], 'contains': ['2420.c1.a1', '3630.b1.b1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [789, -1, 338, -1, 9528, -1, 8924, -1], 'generators': [14535, 80, 30, 60], 'label': '29040.c.1210.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '10.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1210.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1210.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028411
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '264.a1.a1', '440.a1.a1', '660.a1.a1'], 'contains': ['2640.a1.a1', '14520.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7394, -1, 9531, -1, 3204, -1, 3403, -1], 'generators': [14520, 2640], 'label': '29040.c.1320.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '1320.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028412
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '264.a1.b1', '440.a1.b1', '660.a1.b1'], 'contains': ['2640.a1.b1', '14520.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7394, -1, 8118, -1, 3204, -1, 3263, -1], 'generators': [14520, 2760], 'label': '29040.c.1320.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '1320.a1.b1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028413
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.a1.a1', '264.a1.c1', '440.a1.c1', '660.a1.c1'], 'contains': ['2640.a1.c1', '14520.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7394, -1, 8616, -1, 3204, -1, 3124, -1], 'generators': [14520, 21240], 'label': '29040.c.1320.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '1320.a1.c1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028414
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '264.b1.a1', '440.b1.a1', '660.a1.a1'], 'contains': ['2640.a1.a1', '14520.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8780, -1, 6401, -1, 4049, -1, 4621, -1], 'generators': [14580, 2640], 'label': '29040.c.1320.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '1320.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028415
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '264.b1.b1', '440.b1.b1', '660.a1.b1'], 'contains': ['2640.a1.b1', '14520.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8780, -1, 3375, -1, 4049, -1, 4426, -1], 'generators': [14580, 2760], 'label': '29040.c.1320.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '1320.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.b1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028416
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.b1.a1', '264.b1.c1', '440.b1.c1', '660.a1.c1'], 'contains': ['2640.a1.c1', '14520.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8780, -1, 5545, -1, 4049, -1, 4285, -1], 'generators': [14580, 21240], 'label': '29040.c.1320.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '1320.b1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.b1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028417
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '264.c1.a1', '440.c1.a1', '660.a1.a1'], 'contains': ['2640.a1.a1', '14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5352, -1, 4714, -1, 5017, -1, 5965, -1], 'generators': [60, 2640], 'label': '29040.c.1320.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '1320.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028418
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '264.c1.b1', '440.c1.b1', '660.a1.b1'], 'contains': ['2640.a1.b1', '14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5352, -1, 2712, -1, 5017, -1, 5668, -1], 'generators': [60, 2760], 'label': '29040.c.1320.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '1320.c1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.c1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028419
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1320.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['120.c1.a1', '264.c1.c1', '440.c1.c1', '660.a1.c1'], 'contains': ['2640.a1.c1', '14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5352, -1, 3535, -1, 5017, -1, 5254, -1], 'generators': [60, 21240], 'label': '29040.c.1320.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '1320.c1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1320.c1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028420
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['4840.a1.a1', '4840.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '3.a1.a1'], 'contains': ['12.c1.a1', '30.b1.b1', '726.b1.b1'], 'core': '6.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1733, 9499, 429, 7131, 7987, 9701, 8138, 8315], 'generators': [14535, 2640, 30, 60, 24, 18600], 'label': '29040.c.6.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '6.b1.b1', 'normal_contained_in': ['2.b1.b1', '3.a1.a1'], 'normal_contains': ['12.c1.a1', '30.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '6.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028421
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1452.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['132.a1.a1', '132.a1.b1', '132.a1.c1', '484.a1.a1', '726.a1.a1'], 'contains': ['2904.a1.a1', '2904.b1.a1', '2904.c1.a1', '7260.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5903, -1, 5045, -1, 6037, -1, 3901, -1], 'generators': [14520, 24, 60], 'label': '29040.c.1452.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1452.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1452.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028422
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1452.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '484.b1.a1', '726.a1.a1'], 'contains': ['2904.c1.a1', '7260.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4097, -1, 2291, -1, 6878, -1, 7382, -1], 'generators': [14550, 60, 24], 'label': '29040.c.1452.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1452.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1452.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028423
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1452.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '484.c1.a1', '726.a1.a1', '726.b1.a1', '726.b1.b1'], 'contains': ['2904.c1.a1', '7260.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3083, -1, 1795, -1, 7632, -1, 7923, -1], 'generators': [30, 60, 24], 'label': '29040.c.1452.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '12.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1452.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1452.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028424
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1815.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['15.a1.a1', '363.a1.a1', '605.a1.a1'], 'contains': ['3630.a1.a1', '3630.b1.a1', '3630.b1.b1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1322, -1, 611, -1, 9259, -1, 9241, -1], 'generators': [15, 14520], 'label': '29040.c.1815.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '15.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1815.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1815.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028425
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '1936.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['176.a1.a1', '176.a1.b1', '176.a1.c1', '968.a1.a1', '968.b1.a1', '968.c1.a1'], 'contains': ['5808.a1.a1', '9680.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8159, -1, 7943, -1, 5231, -1, 1881, -1], 'generators': [80, 24], 'label': '29040.c.1936.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '1936.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1936.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028426
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2420.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['220.a1.a1', '220.a1.b1', '220.a1.c1', '484.a1.a1', '1210.a1.a1'], 'contains': ['4840.a1.a1', '4840.b1.a1', '4840.c1.a1', '7260.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5041, -1, 3732, -1, 6397, -1, 6249, -1], 'generators': [14520, 60, 80], 'label': '29040.c.2420.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2420.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2420.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028427
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2420.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.b1.a1', '484.b1.a1', '1210.a1.a1'], 'contains': ['4840.c1.a1', '7260.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3877, -1, 2032, -1, 7180, -1, 7521, -1], 'generators': [14550, 80, 60], 'label': '29040.c.2420.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2420.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2420.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028428
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2420.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.c1.a1', '484.c1.a1', '1210.a1.a1', '1210.b1.a1', '1210.b1.b1'], 'contains': ['4840.c1.a1', '7260.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2358, -1, 1213, -1, 8277, -1, 8321, -1], 'generators': [30, 80, 60], 'label': '29040.c.2420.c1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '20.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2420.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2420.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028429
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '528.a1.a1', '880.a1.a1', '1320.a1.a1', '1320.b1.a1', '1320.c1.a1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7786, -1, 7743, -1, 3836, -1, 3979, -1], 'generators': [2640], 'label': '29040.c.2640.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '2640.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2640.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028430
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '528.a1.b1', '880.a1.b1', '1320.a1.b1', '1320.b1.b1', '1320.c1.b1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7786, -1, 6168, -1, 3836, -1, 3839, -1], 'generators': [2760], 'label': '29040.c.2640.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '2640.a1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2640.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028431
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['3630.b1.a1', '3630.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1', '88.a1.a1', '88.a1.b1', '88.a1.c1'], 'core': '8.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7632, 501, 8302, 599, 1211, 442, 1237, 406], 'generators': [14520, 24, 2760, 80, 2640], 'label': '29040.c.8.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.a1.a1', '40.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': '8.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028432
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2640.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['240.a1.a1', '528.a1.c1', '880.a1.c1', '1320.a1.c1', '1320.b1.c1', '1320.c1.c1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [7786, -1, 7290, -1, 3836, -1, 3700, -1], 'generators': [21240], 'label': '29040.c.2640.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '2640.a1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2640.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028433
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2904.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['264.a1.a1', '264.a1.b1', '264.a1.c1', '968.a1.a1', '1452.a1.a1'], 'contains': ['5808.a1.a1', '14520.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [6998, -1, 9285, -1, 4630, -1, 895, -1], 'generators': [14520, 24], 'label': '29040.c.2904.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2904.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2904.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028434
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2904.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['264.b1.a1', '264.b1.b1', '264.b1.c1', '968.b1.a1', '1452.a1.a1'], 'contains': ['5808.a1.a1', '14520.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [9443, -1, 6685, -1, 5442, -1, 2652, -1], 'generators': [14580, 24], 'label': '29040.c.2904.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2904.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2904.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028435
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2904.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['264.c1.a1', '264.c1.b1', '264.c1.c1', '968.c1.a1', '1452.a1.a1', '1452.b1.a1', '1452.c1.a1'], 'contains': ['5808.a1.a1', '14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5450, -1, 4185, -1, 6222, -1, 5397, -1], 'generators': [60, 24], 'label': '29040.c.2904.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '2904.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2904.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028436
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '3630.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.a1.a1', '726.a1.a1', '1210.a1.a1', '1815.a1.a1'], 'contains': ['7260.a1.a1', '7260.b1.a1', '7260.c1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2074, -1, 1494, -1, 7900, -1, 8122, -1], 'generators': [14520, 30], 'label': '29040.c.3630.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '30.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '3630.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3630.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028437
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '3630.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.a1', '726.b1.a1', '1210.b1.a1', '1815.a1.a1'], 'contains': ['7260.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1038, -1, 781, -1, 9050, -1, 9241, -1], 'generators': [15], 'label': '29040.c.3630.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '30.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '3630.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3630.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028438
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '3630.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['30.b1.b1', '726.b1.b1', '1210.b1.b1', '1815.a1.a1'], 'contains': ['7260.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1038, -1, 458, -1, 9050, -1, 8824, -1], 'generators': [14535], 'label': '29040.c.3630.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '30.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '3630.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3630.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028439
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4840.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['6.b1.a1', '6.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['440.a1.a1', '440.a1.b1', '440.a1.c1', '968.a1.a1', '2420.a1.a1'], 'contains': ['9680.a1.a1', '14520.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6613, 1138, 8839, 521, 4822, 1330, 2997, 1222], 'generators': [14520, 80], 'label': '29040.c.4840.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '4840.a1.a1', 'normal_contained_in': ['40.a1.a1'], 'normal_contains': ['9680.a1.a1', '14520.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4840.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4840.c', 'quotient_action_kernel_order': 4840, 'quotient_fusion': None, 'short_label': '4840.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028440
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4840.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['440.b1.a1', '440.b1.b1', '440.b1.c1', '968.b1.a1', '2420.a1.a1'], 'contains': ['9680.a1.a1', '14520.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8995, -1, 5815, -1, 5634, -1, 4156, -1], 'generators': [14580, 80], 'label': '29040.c.4840.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '4840.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4840.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028441
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4840.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['440.c1.a1', '440.c1.b1', '440.c1.c1', '968.c1.a1', '2420.a1.a1', '2420.b1.a1', '2420.c1.a1'], 'contains': ['9680.a1.a1', '14520.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4508, -1, 3064, -1, 6414, -1, 6249, -1], 'generators': [60, 80], 'label': '29040.c.4840.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '4840.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4840.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028442
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['3630.b1.a1', '3630.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['16.a1.a1', '24.b1.a1', '40.b1.a1', '88.b1.a1', '88.b1.b1', '88.b1.c1'], 'core': '8.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8858, 1668, 6471, 1749, 2136, 1362, 2392, 1251], 'generators': [14580, 24, 2760, 80, 2640], 'label': '29040.c.8.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': ['4.a1.a1'], 'normal_contains': ['16.a1.a1', '24.b1.a1', '40.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': '8.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028443
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '5808.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['528.a1.a1', '528.a1.b1', '528.a1.c1', '1936.a1.a1', '2904.a1.a1', '2904.b1.a1', '2904.c1.a1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8394, -1, 8031, -1, 5077, -1, 2394, -1], 'generators': [24], 'label': '29040.c.5808.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '5808.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5808.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028444
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '7260.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['660.a1.a1', '660.a1.b1', '660.a1.c1', '1452.a1.a1', '2420.a1.a1', '3630.a1.a1'], 'contains': ['14520.a1.a1', '14520.b1.a1', '14520.c1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5903, -1, 3899, -1, 6018, -1, 5532, -1], 'generators': [14520, 60], 'label': '29040.c.7260.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '7260.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7260.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028445
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '7260.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.b1.a1', '1452.b1.a1', '2420.b1.a1', '3630.a1.a1'], 'contains': ['14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3672, -1, 1989, -1, 7029, -1, 7382, -1], 'generators': [14550], 'label': '29040.c.7260.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '7260.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7260.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028446
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '7260.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.c1.a1', '1452.c1.a1', '2420.c1.a1', '3630.a1.a1', '3630.b1.a1', '3630.b1.b1'], 'contains': ['14520.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2185, -1, 1171, -1, 7766, -1, 8321, -1], 'generators': [30], 'label': '29040.c.7260.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '60.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '7260.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '7260.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028447
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '9680.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['3.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['880.a1.a1', '880.a1.b1', '880.a1.c1', '1936.a1.a1', '4840.a1.a1', '4840.b1.a1', '4840.c1.a1'], 'contains': ['29040.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8064, 1052, 7458, 1257, 5250, 1856, 3573, 1705], 'generators': [80], 'label': '29040.c.9680.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '9680.a1.a1', 'normal_contained_in': ['80.a1.a1', '4840.a1.a1'], 'normal_contains': ['29040.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '9680.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': '1.1', 'quotient_action_kernel': '9680.a', 'quotient_action_kernel_order': 9680, 'quotient_fusion': None, 'short_label': '9680.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028448
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '14520.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['2.b1.a1', '2.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1320.a1.a1', '1320.a1.b1', '1320.a1.c1', '2904.a1.a1', '4840.a1.a1', '7260.a1.a1'], 'contains': ['29040.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6792, 1428, 8839, 789, 4822, 2197, 3263, 2019], 'generators': [14520], 'label': '29040.c.14520.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '14520.a1.a1', 'normal_contained_in': ['120.a1.a1', '4840.a1.a1'], 'normal_contains': ['29040.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '14520.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': '1.1', 'quotient_action_kernel': '14520.d', 'quotient_action_kernel_order': 14520, 'quotient_fusion': None, 'short_label': '14520.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028449
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '14520.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1320.b1.a1', '1320.b1.b1', '1320.b1.c1', '2904.b1.a1', '4840.b1.a1', '7260.a1.a1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [8995, -1, 5815, -1, 5442, -1, 4285, -1], 'generators': [14580], 'label': '29040.c.14520.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '14520.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14520.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028450
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '14520.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1320.c1.a1', '1320.c1.b1', '1320.c1.c1', '2904.c1.a1', '4840.c1.a1', '7260.a1.a1', '7260.b1.a1', '7260.c1.a1'], 'contains': ['29040.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [4756, -1, 3032, -1, 6222, -1, 5668, -1], 'generators': [60], 'label': '29040.c.14520.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '120.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '14520.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14520.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028451
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '29040.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': ['2640.a1.a1', '2640.a1.b1', '2640.a1.c1', '5808.a1.a1', '9680.a1.a1', '14520.a1.a1', '14520.b1.a1', '14520.c1.a1'], 'contains': [], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7838, 1428, 7361, 1257, 5163, 2197, 3769, 2019], 'generators': [], 'label': '29040.c.29040.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '29040.a1.a1', 'normal_contained_in': ['240.a1.a1', '9680.a1.a1', '14520.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '29040.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '29040.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028452
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '4.b1.a1', '4.c1.a1'], 'contains': ['16.a1.a1', '24.c1.a1', '40.c1.a1', '88.c1.a1', '88.c1.b1', '88.c1.c1'], 'core': '8.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5705, 3444, 3367, 3645, 4724, 3222, 5321, 2960], 'generators': [60, 24, 2760, 80, 2640], 'label': '29040.c.8.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': ['4.a1.a1', '4.c1.a1', '4.b1.a1'], 'normal_contains': ['16.a1.a1', '24.c1.a1', '40.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '8.c1.a1', 'projective_image': '9680.a', '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': '4840.c'}
-
id: 65028453
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '5.a1.a1'], 'contains': ['20.a1.a1', '20.b1.a1', '20.c1.a1', '30.a1.a1', '1210.a1.a1'], 'core': '10.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3662, 7259, 1976, 6647, 6813, 5186, 7805, 4167], 'generators': [14520, 2640, 80, 60, 30, 15960], 'label': '29040.c.10.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1.a1', 'normal_contained_in': ['2.a1.a1', '5.a1.a1'], 'normal_contains': ['20.a1.a1', '20.c1.a1', '20.b1.a1', '30.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028454
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['2904.a1.a1', '2904.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.b1.a1', '1210.b1.a1'], 'core': '10.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1070, 8643, 949, 9397, 9053, 8070, 9844, 7610], 'generators': [15, 2640, 30, 60, 80, 18600], 'label': '29040.c.10.b1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.a1', 'normal_contained_in': ['2.b1.a1', '5.a1.a1'], 'normal_contains': ['20.c1.a1', '30.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': '5.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '10.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028455
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '10.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['2904.a1.a1', '2904.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '5.a1.a1'], 'contains': ['20.c1.a1', '30.b1.b1', '1210.b1.b1'], 'core': '10.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1070, 8643, 257, 8158, 9053, 8070, 8502, 6817], 'generators': [14535, 2640, 30, 60, 80, 18600], 'label': '29040.c.10.b1.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.b1.b1', 'normal_contained_in': ['2.b1.b1', '5.a1.a1'], 'normal_contains': ['20.c1.a1', '30.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '10.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': '5.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '10.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028456
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.a1.a1', '24.b1.a1', '24.c1.a1', '60.a1.a1', '132.a1.a1', '132.a1.b1', '132.a1.c1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6926, 2731, 4659, 2461, 3091, 4194, 4053, 3853], 'generators': [14520, 24, 2760, 60, 2640], 'label': '29040.c.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['24.a1.a1', '24.c1.a1', '24.b1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028457
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.b1.a1', '4.c1.a1', '6.a1.a1', '10.a1.a1', '242.a1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3303, 6297, 2178, 5585, 6813, 5708, 7029, 4625], 'generators': [14520, 2760, 80, 24, 30, 2640, 60], 'label': '29040.c.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', '4.c1.a1', '4.b1.a1', '6.a1.a1', '10.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028458
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.a1.a1'], 'contains': ['24.c1.a1', '60.b1.a1', '1452.b1.a1'], 'core': '12.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5054, 5063, 2928, 4143, 5216, 6029, 6281, 5540], 'generators': [14550, 60, 15960, 24, 2640], 'label': '29040.c.12.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.b1.a1', 'normal_contained_in': ['4.b1.a1', '6.a1.a1'], 'normal_contains': ['24.c1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.b1.a1', 'projective_image': '29040.c', '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': '4840.c'}
-
id: 65028459
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.a1.a1', '6.b1.a1', '6.b1.b1'], 'contains': ['24.c1.a1', '60.c1.a1', '1452.c1.a1'], 'core': '12.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3149, 6327, 1708, 5741, 6313, 8729, 7385, 8020], 'generators': [30, 60, 2760, 24, 2640], 'label': '29040.c.12.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '12.c1.a1', 'normal_contained_in': ['4.c1.a1', '6.a1.a1', '6.b1.b1', '6.b1.a1'], 'normal_contains': ['24.c1.a1', '60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '29040.c', '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': '4840.c'}
-
id: 65028460
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '15.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['1936.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '5.a1.a1'], 'contains': ['30.a1.a1', '30.b1.a1', '30.b1.b1', '1815.a1.a1'], 'core': '15.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1779, 9178, 603, 8899, 8537, 8934, 9441, 9020], 'generators': [15, 2640, 30, 60, 14520, 18600], 'label': '29040.c.15.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '15.a1.a1', 'normal_contained_in': ['3.a1.a1', '5.a1.a1'], 'normal_contains': ['30.a1.a1', '30.b1.b1', '30.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '15.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': '5.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '15.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028461
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['1815.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.b1.a1', '8.c1.a1'], 'contains': ['48.a1.a1', '80.a1.a1', '176.a1.a1', '176.a1.b1', '176.a1.c1'], 'core': '16.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8858, 1148, 7443, 1160, 1211, 1161, 1578, 1067], 'generators': [80, 2760, 2640, 24], 'label': '29040.c.16.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': ['8.a1.a1', '8.c1.a1', '8.b1.a1'], 'normal_contains': ['48.a1.a1', '80.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': '8.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028462
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '20.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '10.a1.a1'], 'contains': ['40.a1.a1', '40.b1.a1', '40.c1.a1', '60.a1.a1', '220.a1.a1', '220.a1.b1', '220.a1.c1'], 'core': '20.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6502, 4494, 4308, 3894, 3648, 2294, 5689, 2107], 'generators': [14520, 80, 2760, 60, 2640], 'label': '29040.c.20.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': ['4.a1.a1', '10.a1.a1'], 'normal_contains': ['40.a1.a1', '40.c1.a1', '40.b1.a1', '60.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028463
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '20.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '10.a1.a1'], 'contains': ['40.c1.a1', '60.b1.a1', '2420.b1.a1'], 'core': '20.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4734, 5700, 2681, 5419, 5720, 5186, 6672, 4765], 'generators': [14550, 60, 15960, 80, 2640], 'label': '29040.c.20.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '20.b1.a1', 'normal_contained_in': ['4.b1.a1', '10.a1.a1'], 'normal_contains': ['40.c1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028464
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '20.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '10.a1.a1', '10.b1.a1', '10.b1.b1'], 'contains': ['40.c1.a1', '60.c1.a1', '2420.c1.a1'], 'core': '20.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3413, 7177, 1700, 7203, 7514, 6873, 8178, 6315], 'generators': [30, 60, 15960, 80, 2640], 'label': '29040.c.20.c1.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.c1.a1', 'normal_contained_in': ['4.c1.a1', '10.a1.a1', '10.b1.b1', '10.b1.a1'], 'normal_contains': ['40.c1.a1', '60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '20.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028465
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '24.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['1210.b1.a1', '1210.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '120.a1.a1', '264.a1.a1', '264.a1.b1', '264.a1.c1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7972, 985, 8519, 541, 237, 2912, 1237, 2676], 'generators': [14520, 2760, 2640, 24], 'label': '29040.c.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['8.a1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '120.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': '8.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028466
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '24.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['1210.b1.a1', '1210.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.a1.a1'], 'contains': ['48.a1.a1', '120.b1.a1', '264.b1.a1', '264.b1.b1', '264.b1.c1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9191, 2345, 6341, 1843, 1670, 3679, 2654, 3381], 'generators': [14580, 2760, 2640, 24], 'label': '29040.c.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['8.b1.a1', '12.a1.a1'], 'normal_contains': ['48.a1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': '8.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028467
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.a1.a1', '12.b1.a1', '12.c1.a1'], 'contains': ['48.a1.a1', '120.c1.a1', '264.c1.a1', '264.c1.b1', '264.c1.c1'], 'core': '24.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5701, 3577, 3794, 3022, 5158, 6126, 6157, 5628], 'generators': [60, 2760, 2640, 24], 'label': '29040.c.24.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': ['8.c1.a1', '12.a1.a1', '12.c1.a1', '12.b1.a1'], 'normal_contains': ['48.a1.a1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.c1.a1', 'projective_image': '29040.c', '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': '4840.c'}
-
id: 65028468
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['14520.a1.a1', '14520.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '6.b1.a1', '10.b1.a1', '242.b1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [969, 7880, 1145, 8777, 8534, 8014, 9138, 7662], 'generators': [15, 18600, 24, 30, 80, 2640, 60], 'label': '29040.c.2.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '6.b1.a1', '10.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': '9680.a', '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': '4840.c'}
-
id: 65028469
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '30.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'contains': ['60.a1.a1', '60.b1.a1', '60.c1.a1', '3630.a1.a1'], 'core': '30.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4011, 7758, 2057, 6185, 6818, 7885, 7718, 7245], 'generators': [14520, 60, 15960, 30, 2640], 'label': '29040.c.30.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '30.a1.a1', 'normal_contained_in': ['6.a1.a1', '10.a1.a1', '15.a1.a1'], 'normal_contains': ['60.a1.a1', '60.c1.a1', '60.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '30.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028470
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['968.a1.a1', '968.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'contains': ['60.c1.a1', '3630.b1.a1'], 'core': '30.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1407, 9010, 954, 9314, 8652, 9347, 9720, 9105], 'generators': [15, 60, 18600, 30, 2640], 'label': '29040.c.30.b1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '30.b1.a1', 'normal_contained_in': ['6.b1.a1', '10.b1.a1', '15.a1.a1'], 'normal_contains': ['60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': '5.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '30.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028471
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '30.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['968.a1.a1', '968.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'contains': ['60.c1.a1', '3630.b1.b1'], 'core': '30.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1407, 9010, 474, 8139, 8652, 9347, 8549, 8588], 'generators': [14535, 60, 18600, 30, 2640], 'label': '29040.c.30.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '30.b1.b1', 'normal_contained_in': ['6.b1.b1', '10.b1.b1', '15.a1.a1'], 'normal_contains': ['60.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '30.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': '5.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '30.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028472
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '40.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': ['726.b1.a1', '726.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '20.a1.a1'], 'contains': ['80.a1.a1', '120.a1.a1', '440.a1.a1', '440.a1.b1', '440.a1.c1'], 'core': '40.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7433, 664, 8314, 419, 724, 345, 2938, 317], 'generators': [14520, 2760, 2640, 80], 'label': '29040.c.40.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': ['8.a1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.a1.a1', '4840.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': '40.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '40.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.2'}
-
id: 65028527
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '88.b1.a1', '220.a1.a1'], 'contains': ['880.a1.a1', '1320.b1.a1', '4840.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9221, -1, 6449, -1, 4049, -1, 4681, -1], 'generators': [14580, 2640, 80], 'label': '29040.c.440.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '440.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028473
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '40.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['726.b1.a1', '726.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '20.a1.a1'], 'contains': ['80.a1.a1', '120.b1.a1', '440.b1.a1', '440.b1.b1', '440.b1.c1'], 'core': '40.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8354, 2681, 5953, 2569, 2136, 2037, 4296, 1871], 'generators': [14580, 2760, 2640, 80], 'label': '29040.c.40.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': ['8.b1.a1', '20.a1.a1'], 'normal_contains': ['80.a1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': '40.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '40.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028474
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '40.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '20.a1.a1', '20.b1.a1', '20.c1.a1'], 'contains': ['80.a1.a1', '120.c1.a1', '440.c1.a1', '440.c1.b1', '440.c1.c1'], 'core': '40.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5531, 5145, 2979, 4527, 5624, 4459, 6815, 4097], 'generators': [60, 2760, 2640, 80], 'label': '29040.c.40.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': ['8.c1.a1', '20.a1.a1', '20.c1.a1', '20.b1.a1'], 'normal_contains': ['80.a1.a1', '120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '40.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '40.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028475
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['88.a1.a1', '88.b1.a1', '88.c1.a1', '132.a1.a1', '220.a1.a1', '484.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6080, -1, 5640, -1, 4109, -1, 3733, -1], 'generators': [14520, 80, 24, 60, 2640], 'label': '29040.c.44.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '44.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028476
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['88.a1.b1', '88.b1.b1', '88.c1.b1', '132.a1.b1', '220.a1.b1', '484.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6080, -1, 4829, -1, 4109, -1, 3476, -1], 'generators': [14520, 80, 24, 60, 2760], 'label': '29040.c.44.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '44.a1.b1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028477
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '44.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1'], 'contains': ['88.a1.c1', '88.b1.c1', '88.c1.c1', '132.a1.c1', '220.a1.c1', '484.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6080, -1, 5105, -1, 4109, -1, 3219, -1], 'generators': [14520, 80, 24, 60, 21240], 'label': '29040.c.44.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '44.a1.c1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '44.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028478
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '48.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['605.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.a1.a1', '24.b1.a1', '24.c1.a1'], 'contains': ['240.a1.a1', '528.a1.a1', '528.a1.b1', '528.a1.c1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9178, 1825, 7692, 1130, 1523, 3282, 2083, 3015], 'generators': [24, 2640, 2760], 'label': '29040.c.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['16.a1.a1', '24.a1.a1', '24.c1.a1', '24.b1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': '8.1', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028479
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['14520.a1.a1', '14520.b1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.c1.a1', '6.b1.b1', '10.b1.b1', '242.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [969, 7880, 191, 7135, 8534, 8014, 8300, 5972], 'generators': [14535, 18600, 24, 30, 80, 2640, 60], 'label': '29040.c.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.c1.a1', '6.b1.b1', '10.b1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028480
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '60.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'contains': ['120.a1.a1', '120.b1.a1', '120.c1.a1', '660.a1.a1', '660.a1.b1', '660.a1.c1'], 'core': '60.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6884, 4005, 4318, 3124, 2666, 5346, 6465, 4912], 'generators': [14520, 2760, 2640, 60], 'label': '29040.c.60.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': ['12.a1.a1', '20.a1.a1', '30.a1.a1'], 'normal_contains': ['120.a1.a1', '120.c1.a1', '120.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028481
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '60.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'contains': ['120.c1.a1', '7260.b1.a1'], 'core': '60.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4633, 6342, 2494, 5347, 6585, 6817, 7191, 6263], 'generators': [14550, 15960, 2640, 60], 'label': '29040.c.60.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '60.b1.a1', 'normal_contained_in': ['12.b1.a1', '20.b1.a1', '30.a1.a1'], 'normal_contains': ['120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028482
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '60.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '20.c1.a1', '30.a1.a1', '30.b1.a1', '30.b1.b1'], 'contains': ['120.c1.a1', '7260.c1.a1'], 'core': '60.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3553, 7758, 1635, 7018, 7401, 7885, 8513, 7632], 'generators': [30, 15960, 2640, 60], 'label': '29040.c.60.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '60.c1.a1', 'normal_contained_in': ['12.c1.a1', '20.c1.a1', '30.a1.a1', '30.b1.b1', '30.b1.a1'], 'normal_contains': ['120.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '60.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '60.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028483
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '80.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': ['363.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '40.a1.a1', '40.b1.a1', '40.c1.a1'], 'contains': ['240.a1.a1', '880.a1.a1', '880.a1.b1', '880.a1.c1'], 'core': '80.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8302, 1749, 7466, 1716, 1920, 1856, 3620, 1705], 'generators': [80, 2640, 2760], 'label': '29040.c.80.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '80.a1.a1', 'normal_contained_in': ['16.a1.a1', '40.a1.a1', '40.c1.a1', '40.b1.a1'], 'normal_contains': ['240.a1.a1', '9680.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '80.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': '40.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '80.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.2'}
-
id: 65028484
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.a1'], 'contains': ['176.a1.a1', '264.a1.a1', '440.a1.a1', '968.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6929, -1, 9554, -1, 3163, -1, 912, -1], 'generators': [14520, 24, 2640, 80], 'label': '29040.c.88.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '88.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028485
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.b1'], 'contains': ['176.a1.b1', '264.a1.b1', '440.a1.b1', '968.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6929, -1, 8116, -1, 3163, -1, 604, -1], 'generators': [14520, 24, 2760, 80], 'label': '29040.c.88.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '88.a1.b1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028486
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '44.a1.c1'], 'contains': ['176.a1.c1', '264.a1.c1', '440.a1.c1', '968.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6929, -1, 9159, -1, 3163, -1, 297, -1], 'generators': [14520, 24, 21240, 80], 'label': '29040.c.88.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '88.a1.c1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028487
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.a1'], 'contains': ['176.a1.a1', '264.b1.a1', '440.b1.a1', '968.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9763, -1, 7073, -1, 3591, -1, 2392, -1], 'generators': [14580, 24, 2640, 80], 'label': '29040.c.88.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '88.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028488
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.b1'], 'contains': ['176.a1.b1', '264.b1.b1', '440.b1.b1', '968.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9763, -1, 6314, -1, 3591, -1, 2135, -1], 'generators': [14580, 24, 2760, 80], 'label': '29040.c.88.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '88.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028489
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '44.a1.c1'], 'contains': ['176.a1.c1', '264.b1.c1', '440.b1.c1', '968.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9763, -1, 6654, -1, 3591, -1, 1878, -1], 'generators': [14580, 24, 21240, 80], 'label': '29040.c.88.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '88.b1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.b1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028490
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['9680.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.b1.b1', '15.a1.a1', '363.a1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1733, 9499, 668, 8095, 7953, 8986, 8754, 8555], 'generators': [15, 18600, 24, 30, 14520, 2640, 60], 'label': '29040.c.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.a1.a1', '6.b1.b1', '6.b1.a1', '15.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': '1.1', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028491
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.a1.a1'], 'contains': ['176.a1.a1', '264.c1.a1', '440.c1.a1', '968.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [4857, -1, 4420, -1, 4762, -1, 5635, -1], 'generators': [60, 24, 2640, 80], 'label': '29040.c.88.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '88.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028492
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.a1.b1'], 'contains': ['176.a1.b1', '264.c1.b1', '440.c1.b1', '968.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [4857, -1, 3480, -1, 4762, -1, 5118, -1], 'generators': [60, 24, 2760, 80], 'label': '29040.c.88.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '88.c1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028493
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '88.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '44.a1.c1'], 'contains': ['176.a1.c1', '264.c1.c1', '440.c1.c1', '968.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [4857, -1, 3886, -1, 4762, -1, 4601, -1], 'generators': [60, 24, 21240, 80], 'label': '29040.c.88.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '88.c1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '88.c1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028494
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '120.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': ['242.b1.a1', '242.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'contains': ['240.a1.a1', '1320.a1.a1', '1320.a1.b1', '1320.a1.c1'], 'core': '120.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7675, 1525, 8572, 605, 1127, 2619, 3319, 2406], 'generators': [14520, 2640, 2760], 'label': '29040.c.120.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '120.a1.a1', 'normal_contained_in': ['24.a1.a1', '40.a1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.a1', '14520.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': '40.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '120.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.2'}
-
id: 65028495
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '120.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['242.b1.a1', '242.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '40.b1.a1', '60.a1.a1'], 'contains': ['240.a1.a1', '1320.b1.a1', '1320.b1.b1', '1320.b1.c1'], 'core': '120.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8629, 3343, 5885, 2398, 2323, 3856, 4927, 3543], 'generators': [14580, 2640, 2760], 'label': '29040.c.120.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.b1.a1', 'normal_contained_in': ['24.b1.a1', '40.b1.a1', '60.a1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': '40.2', 'quotient_action_kernel': '3.1', 'quotient_action_kernel_order': 3, 'quotient_fusion': None, 'short_label': '120.b1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028496
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '120.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '40.c1.a1', '60.a1.a1', '60.b1.a1', '60.c1.a1'], 'contains': ['240.a1.a1', '1320.c1.a1', '1320.c1.b1', '1320.c1.c1'], 'core': '120.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5505, 4905, 3016, 4031, 5454, 5736, 7136, 5270], 'generators': [60, 2640, 2760], 'label': '29040.c.120.c1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '120.c1.a1', 'normal_contained_in': ['24.c1.a1', '40.c1.a1', '60.a1.a1', '60.c1.a1', '60.b1.a1'], 'normal_contains': ['240.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '120.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028497
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '121.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['242.a1.a1', '242.b1.a1', '242.b1.b1', '363.a1.a1', '605.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [819, -1, 927, -1, 9519, -1, 8809, -1], 'generators': [15, 60, 80, 24, 14520, 30], 'label': '29040.c.121.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '121.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '121.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028498
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.a1'], 'contains': ['264.a1.a1', '264.b1.a1', '264.c1.a1', '660.a1.a1', '1452.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6462, -1, 5540, -1, 3980, -1, 3991, -1], 'generators': [14520, 24, 2640, 60], 'label': '29040.c.132.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '132.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028499
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.b1'], 'contains': ['264.a1.b1', '264.b1.b1', '264.c1.b1', '660.a1.b1', '1452.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6462, -1, 4536, -1, 3980, -1, 3474, -1], 'generators': [14520, 24, 2760, 60], 'label': '29040.c.132.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '132.a1.b1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028500
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '132.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '44.a1.c1'], 'contains': ['264.a1.c1', '264.b1.c1', '264.c1.c1', '660.a1.c1', '1452.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6462, -1, 4877, -1, 3980, -1, 3217, -1], 'generators': [14520, 24, 21240, 60], 'label': '29040.c.132.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '132.a1.c1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '132.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028501
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.a1.a1', '8.b1.a1', '8.c1.a1', '12.a1.a1', '20.a1.a1', '44.a1.a1', '44.a1.b1', '44.a1.c1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6468, 2559, 5430, 2744, 3648, 2760, 3733, 2277], 'generators': [14520, 2640, 80, 24, 60, 2760], 'label': '29040.c.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.a1.a1', '8.c1.a1', '8.b1.a1', '12.a1.a1', '20.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028502
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '176.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.a1', '88.b1.a1', '88.c1.a1'], 'contains': ['528.a1.a1', '880.a1.a1', '1936.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8675, -1, 8640, -1, 3408, -1, 1818, -1], 'generators': [80, 2640, 24], 'label': '29040.c.176.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '176.a1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028503
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '176.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.b1', '88.b1.b1', '88.c1.b1'], 'contains': ['528.a1.b1', '880.a1.b1', '1936.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8675, -1, 7138, -1, 3408, -1, 1510, -1], 'generators': [80, 2760, 24], 'label': '29040.c.176.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '176.a1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028504
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '176.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '88.a1.c1', '88.b1.c1', '88.c1.c1'], 'contains': ['528.a1.c1', '880.a1.c1', '1936.a1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8675, -1, 7987, -1, 3408, -1, 1203, -1], 'generators': [80, 21240, 24], 'label': '29040.c.176.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '176.a1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '176.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028505
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.a1'], 'contains': ['440.a1.a1', '440.b1.a1', '440.c1.a1', '660.a1.a1', '2420.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6038, -1, 5345, -1, 4371, -1, 5893, -1], 'generators': [14520, 80, 2640, 60], 'label': '29040.c.220.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '220.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028506
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.b1'], 'contains': ['440.a1.b1', '440.b1.b1', '440.c1.b1', '660.a1.b1', '2420.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6038, -1, 2872, -1, 4371, -1, 5376, -1], 'generators': [14520, 80, 2760, 60], 'label': '29040.c.220.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '220.a1.b1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028507
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '220.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['20.a1.a1', '44.a1.c1'], 'contains': ['440.a1.c1', '440.b1.c1', '440.c1.c1', '660.a1.c1', '2420.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6038, -1, 3863, -1, 4371, -1, 4859, -1], 'generators': [14520, 80, 21240, 60], 'label': '29040.c.220.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '20.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '220.a1.c1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '220.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028508
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '240.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': ['121.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.b1.a1', '120.c1.a1'], 'contains': ['2640.a1.a1', '2640.a1.b1', '2640.a1.c1'], 'core': '240.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7923, 2609, 7333, 1716, 2121, 2948, 3979, 2709], 'generators': [2760, 2640], 'label': '29040.c.240.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '240.a1.a1', 'normal_contained_in': ['48.a1.a1', '80.a1.a1', '120.a1.a1', '120.c1.a1', '120.b1.a1'], 'normal_contains': ['29040.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '240.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': '40.2', 'quotient_action_kernel': '6.2', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '240.a1.a1', 'subgroup_fusion': None, 'weyl_group': '40.2'}
-
id: 65028509
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '242.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '121.a1.a1'], 'contains': ['484.a1.a1', '484.b1.a1', '484.c1.a1', '726.a1.a1', '1210.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2773, -1, 2119, -1, 8104, -1, 7002, -1], 'generators': [14520, 80, 24, 30, 60], 'label': '29040.c.242.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028510
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '242.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.a1', '121.a1.a1'], 'contains': ['484.c1.a1', '726.b1.a1', '1210.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [913, -1, 1106, -1, 9514, -1, 9212, -1], 'generators': [15, 24, 30, 80, 60], 'label': '29040.c.242.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028511
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '242.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1.b1', '121.a1.a1'], 'contains': ['484.c1.a1', '726.b1.b1', '1210.b1.b1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [913, -1, 540, -1, 9514, -1, 8738, -1], 'generators': [14535, 24, 30, 80, 60], 'label': '29040.c.242.b1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '242.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '242.b1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028512
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.c1.a1', '12.b1.a1', '20.b1.a1', '484.b1.a1'], 'core': '4.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4845, 4351, 2681, 4050, 5639, 4194, 6442, 3255], 'generators': [14550, 2640, 24, 60, 80, 15960], 'label': '29040.c.4.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.c1.a1', '12.b1.a1', '20.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.b1.a1', 'projective_image': '9680.a', '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': '4840.c'}
-
id: 65028513
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1'], 'contains': ['528.a1.a1', '1320.a1.a1', '2904.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [7544, -1, 9809, -1, 2731, -1, 895, -1], 'generators': [14520, 2640, 24], 'label': '29040.c.264.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028514
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.b1', '132.a1.b1'], 'contains': ['528.a1.b1', '1320.a1.b1', '2904.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [7544, -1, 8242, -1, 2731, -1, 587, -1], 'generators': [14520, 2760, 24], 'label': '29040.c.264.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '264.a1.b1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028515
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.c1', '132.a1.c1'], 'contains': ['528.a1.c1', '1320.a1.c1', '2904.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [7544, -1, 9156, -1, 2731, -1, 279, -1], 'generators': [14520, 21240, 24], 'label': '29040.c.264.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '264.a1.c1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028516
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.b1.a1', '132.a1.a1'], 'contains': ['528.a1.a1', '1320.b1.a1', '2904.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9675, -1, 6752, -1, 3747, -1, 2679, -1], 'generators': [14580, 2640, 24], 'label': '29040.c.264.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '264.b1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028517
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.b1.b1', '132.a1.b1'], 'contains': ['528.a1.b1', '1320.b1.b1', '2904.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9675, -1, 5928, -1, 3747, -1, 2541, -1], 'generators': [14580, 2760, 24], 'label': '29040.c.264.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '264.b1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028518
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '88.b1.c1', '132.a1.c1'], 'contains': ['528.a1.c1', '1320.b1.c1', '2904.b1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9675, -1, 6510, -1, 3747, -1, 2403, -1], 'generators': [14580, 21240, 24], 'label': '29040.c.264.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '264.b1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.b1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028519
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.c1.a1', '132.a1.a1'], 'contains': ['528.a1.a1', '1320.c1.a1', '2904.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5584, -1, 4445, -1, 4779, -1, 5671, -1], 'generators': [60, 2640, 24], 'label': '29040.c.264.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '264.c1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028520
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.c1.b1', '132.a1.b1'], 'contains': ['528.a1.b1', '1320.c1.b1', '2904.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5584, -1, 3281, -1, 4779, -1, 5392, -1], 'generators': [60, 2760, 24], 'label': '29040.c.264.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '264.c1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028521
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '264.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '88.c1.c1', '132.a1.c1'], 'contains': ['528.a1.c1', '1320.c1.c1', '2904.c1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5584, -1, 4144, -1, 4779, -1, 5113, -1], 'generators': [60, 21240, 24], 'label': '29040.c.264.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '264.c1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '264.c1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028522
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '363.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '121.a1.a1'], 'contains': ['726.a1.a1', '726.b1.a1', '726.b1.b1', '1815.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [1368, -1, 893, -1, 9017, -1, 9006, -1], 'generators': [15, 24, 30, 14520, 60], 'label': '29040.c.363.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '3.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '363.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '363.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028523
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '2.b1.a1', '2.b1.b1'], 'contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1', '484.c1.a1'], 'core': '4.c1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2701, 5939, 1554, 6360, 7406, 6178, 7413, 5078], 'generators': [30, 2640, 24, 60, 80, 2760], 'label': '29040.c.4.c1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1.a1', 'normal_contained_in': ['2.a1.a1', '2.b1.b1', '2.b1.a1'], 'normal_contains': ['8.c1.a1', '12.c1.a1', '20.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.c1.a1', 'projective_image': '9680.a', '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': '4840.c'}
-
id: 65028524
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '88.a1.a1', '220.a1.a1'], 'contains': ['880.a1.a1', '1320.a1.a1', '4840.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6998, -1, 9780, -1, 3070, -1, 3098, -1], 'generators': [14520, 2640, 80], 'label': '29040.c.440.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '440.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.a1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028525
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '88.a1.b1', '220.a1.b1'], 'contains': ['880.a1.b1', '1320.a1.b1', '4840.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6998, -1, 8087, -1, 3070, -1, 2959, -1], 'generators': [14520, 2760, 80], 'label': '29040.c.440.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '440.a1.b1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.b1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028526
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '40.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.a1.a1', '88.a1.c1', '220.a1.c1'], 'contains': ['880.a1.c1', '1320.a1.c1', '4840.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [6998, -1, 8755, -1, 3070, -1, 2819, -1], 'generators': [14520, 21240, 80], 'label': '29040.c.440.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.a1.a1', 'old_label': '440.a1.c1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.a1.c1', 'subgroup_fusion': None, 'weyl_group': '10.2'}
-
id: 65028528
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '88.b1.b1', '220.a1.b1'], 'contains': ['880.a1.b1', '1320.b1.b1', '4840.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9221, -1, 5307, -1, 4049, -1, 4421, -1], 'generators': [14580, 2760, 80], 'label': '29040.c.440.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '440.b1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.b1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028529
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.b1.a1', '88.b1.c1', '220.a1.c1'], 'contains': ['880.a1.c1', '1320.b1.c1', '4840.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [9221, -1, 5846, -1, 4049, -1, 4161, -1], 'generators': [14580, 21240, 80], 'label': '29040.c.440.b1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '440.b1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.b1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028530
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '88.c1.a1', '220.a1.a1'], 'contains': ['880.a1.a1', '1320.c1.a1', '4840.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5211, -1, 4510, -1, 5082, -1, 6890, -1], 'generators': [60, 2640, 80], 'label': '29040.c.440.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '440.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.c1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028531
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '88.c1.b1', '220.a1.b1'], 'contains': ['880.a1.b1', '1320.c1.b1', '4840.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5211, -1, 2528, -1, 5082, -1, 6630, -1], 'generators': [60, 2760, 80], 'label': '29040.c.440.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '440.c1.b1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.c1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028532
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '440.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['40.c1.a1', '88.c1.c1', '220.a1.c1'], 'contains': ['880.a1.c1', '1320.c1.c1', '4840.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [5211, -1, 3389, -1, 5082, -1, 5871, -1], 'generators': [60, 21240, 80], 'label': '29040.c.440.c1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '40.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '440.c1.c1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '440.c1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028533
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '484.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['44.a1.a1', '44.a1.b1', '44.a1.c1', '242.a1.a1'], 'contains': ['968.a1.a1', '968.b1.a1', '968.c1.a1', '1452.a1.a1', '2420.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [5842, -1, 4919, -1, 6085, -1, 3733, -1], 'generators': [14520, 80, 24, 60], 'label': '29040.c.484.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '484.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '484.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028534
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': ['5808.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.b1.b1', '15.a1.a1', '605.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1194, 8593, 451, 9581, 9084, 7094, 9501, 6817], 'generators': [15, 18600, 80, 30, 14520, 2640, 60], 'label': '29040.c.5.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.b1', '10.b1.a1', '15.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': '5.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4840.c'}
-
id: 65028535
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '484.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '242.a1.a1'], 'contains': ['968.c1.a1', '1452.b1.a1', '2420.b1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3848, -1, 2291, -1, 6993, -1, 7402, -1], 'generators': [14550, 24, 60, 80], 'label': '29040.c.484.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '484.b1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '484.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028536
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '484.c1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '242.a1.a1', '242.b1.a1', '242.b1.b1'], 'contains': ['968.c1.a1', '1452.c1.a1', '2420.c1.a1'], 'core': '9680.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [2466, -1, 1774, -1, 8688, -1, 7923, -1], 'generators': [30, 24, 60, 80], 'label': '29040.c.484.c1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '484.c1.a1', 'projective_image': '9680.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '484.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 65028537
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '528.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.a1', '264.a1.a1', '264.b1.a1', '264.c1.a1'], 'contains': ['2640.a1.a1', '5808.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8789, -1, 8896, -1, 3586, -1, 2488, -1], 'generators': [24, 2640], 'label': '29040.c.528.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '528.a1.a1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
-
id: 65028538
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '528.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.b1', '264.a1.b1', '264.b1.b1', '264.c1.b1'], 'contains': ['2640.a1.b1', '5808.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8789, -1, 7144, -1, 3586, -1, 2299, -1], 'generators': [24, 2760], 'label': '29040.c.528.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '528.a1.b1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 65028539
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '528.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '176.a1.c1', '264.a1.c1', '264.b1.c1', '264.c1.c1'], 'contains': ['2640.a1.c1', '5808.a1.a1'], 'core': '29040.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [8789, -1, 7916, -1, 3586, -1, 2110, -1], 'generators': [24, 21240], 'label': '29040.c.528.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '528.a1.c1', 'projective_image': '29040.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '528.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 65028540
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '605.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['5.a1.a1', '121.a1.a1'], 'contains': ['1210.a1.a1', '1210.b1.a1', '1210.b1.b1', '1815.a1.a1'], 'core': '4840.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [237, -1, 338, -1, 9826, -1, 9418, -1], 'generators': [15, 60, 14520, 80, 30], 'label': '29040.c.605.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '5.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '605.a1.a1', 'projective_image': '4840.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '605.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 65028541
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '660.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '132.a1.a1', '220.a1.a1'], 'contains': ['1320.a1.a1', '1320.b1.a1', '1320.c1.a1', '7260.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6296, -1, 5350, -1, 4354, -1, 6428, -1], 'generators': [14520, 2640, 60], 'label': '29040.c.660.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.a1', 'old_label': '660.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 65028542
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '660.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '132.a1.b1', '220.a1.b1'], 'contains': ['1320.a1.b1', '1320.b1.b1', '1320.c1.b1', '7260.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6296, -1, 2744, -1, 4354, -1, 5532, -1], 'generators': [14520, 2760, 60], 'label': '29040.c.660.a1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.b1', 'old_label': '660.a1.b1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.a1.b1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 65028543
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '660.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4840.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['60.a1.a1', '132.a1.c1', '220.a1.c1'], 'contains': ['1320.a1.c1', '1320.b1.c1', '1320.c1.c1', '7260.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 44, 'diagramx': [6296, -1, 4076, -1, 4354, -1, 5253, -1], 'generators': [14520, 21240, 60], 'label': '29040.c.660.a1.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '60.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '44.a1.c1', 'old_label': '660.a1.c1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '660.a1.c1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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id: 65028544
{'ambient': '29040.c', 'aut_centralizer_order': None, 'aut_label': '726.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '121.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '242.a1.a1', '363.a1.a1'], 'contains': ['1452.a1.a1', '1452.b1.a1', '1452.c1.a1', '3630.a1.a1'], 'core': '14520.a1.a1', 'coset_action_label': None, 'count': 121, 'diagramx': [3022, -1, 2010, -1, 7900, -1, 7662, -1], 'generators': [14520, 24, 60, 30], 'label': '29040.c.726.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '121.a1.a1', 'old_label': '726.a1.a1', 'projective_image': '14520.d', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '726.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}