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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '224.189', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 4, 2], 'aut_gens': [[1, 2, 4, 16], [336, 458, 340, 305], [344, 346, 348, 657], [337, 339, 340, 208], [1, 2, 349, 16]], 'aut_group': None, 'aut_hash': 2377435179119701334, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 55296, 'aut_permdeg': 38, 'aut_perms': [3269876169953629314207046414663349417638139, 2435625643379396466612149971099558651998981, 13601400348425363060504856351187815689456357, 468350242803495473372752126370697596462773826], 'aut_phi_ratio': 288.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 3, 8, 1], [3, 2, 1, 1], [4, 1, 8, 1], [4, 3, 8, 1], [6, 2, 1, 1], [6, 2, 6, 1], [7, 1, 6, 1], [12, 2, 8, 1], [14, 1, 6, 1], [14, 1, 36, 1], [14, 3, 48, 1], [21, 2, 6, 1], [28, 1, 48, 1], [28, 3, 48, 1], [42, 2, 6, 1], [42, 2, 36, 1], [84, 2, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.C_3^3.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': None, 'autcent_hash': 81491427880784167, 'autcent_nilpotent': False, 'autcent_order': 9216, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_6\\times C_2^4.C_2^4.S_3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 3, 8], [3, 2, 1], [4, 1, 8], [4, 3, 8], [6, 2, 7], [7, 1, 6], [12, 2, 8], [14, 1, 42], [14, 3, 48], [21, 2, 6], [28, 1, 48], [28, 3, 48], [42, 2, 42], [84, 2, 48]], 'center_label': '112.37', 'center_order': 112, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1219, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['4.1', 1], ['6.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 3, 1, 8], [3, 2, 1, 1], [4, 1, 2, 4], [4, 3, 2, 4], [6, 2, 1, 7], [7, 1, 6, 1], [12, 2, 2, 4], [14, 1, 6, 7], [14, 3, 6, 8], [21, 2, 6, 1], [28, 1, 12, 4], [28, 3, 12, 4], [42, 2, 6, 7], [84, 2, 12, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1092000, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.226', 'hash': 1219, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [1, 2, 1, 3], 'inner_gens': [[1, 2, 4, 16], [1, 2, 4, 464], [1, 2, 4, 16], [1, 226, 4, 16]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 224], [2, 112]], 'label': '672.1219', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C84:C2^3', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 336, 'number_divisions': 72, 'number_normal_subgroups': 290, 'number_subgroup_autclasses': 84, 'number_subgroup_classes': 472, 'number_subgroups': 836, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 2], [4, 32], [6, 14], [7, 6], [12, 16], [14, 186], [21, 12], [28, 192], [42, 84], [84, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 4, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[337, 11, 341, 265], [1, 347, 5, 209], [337, 346, 340, 545]], 'outer_group': None, 'outer_hash': 81491427880784167, 'outer_nilpotent': False, 'outer_order': 9216, 'outer_permdeg': 21, 'outer_perms': [250823713809738474, 14866667519306821085, 737716648661359422], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4.C_2^4.(C_6\\times S_3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 7], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 4], [6, 16], [12, 16], [24, 4]], 'representations': {'PC': {'code': 69163819449605635671203339, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 58, 8131, 102, 5388, 166]}, 'GLZN': {'d': 2, 'p': 70, 'gens': [343701, 2232012, 345451, 343029, 9947029, 516986, 23667069]}, 'Perm': {'d': 18, 'gens': [3669240, 3669127, 3669136, 8023703, 378011776665600, 3669120, 840]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 28], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{84}:C_2^3', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
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gps_conj_classes • Show schema
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id: 139887303
{'aut_label': '1A', 'centralizer': '1.a1', 'counter': 1, 'group_counter': 1219, 'group_order': 672, 'label': '1A', 'order': 1, 'powers': [1, 1, 1], 'representative': 0, 'size': 1}
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id: 139887414
{'aut_label': '2A', 'centralizer': '1.a1', 'counter': 2, 'group_counter': 1219, 'group_order': 672, 'label': '2A', 'order': 2, 'powers': [1, 2, 2], 'representative': 8, 'size': 1}
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id: 139887525
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 3, 'group_counter': 1219, 'group_order': 672, 'label': '2B', 'order': 2, 'powers': [1, 3, 3], 'representative': 336, 'size': 1}
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id: 139887573
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 4, 'group_counter': 1219, 'group_order': 672, 'label': '2C', 'order': 2, 'powers': [1, 4, 4], 'representative': 344, 'size': 1}
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id: 139887584
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 5, 'group_counter': 1219, 'group_order': 672, 'label': '2D', 'order': 2, 'powers': [1, 5, 5], 'representative': 1, 'size': 1}
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id: 139887595
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 6, 'group_counter': 1219, 'group_order': 672, 'label': '2E', 'order': 2, 'powers': [1, 6, 6], 'representative': 337, 'size': 1}
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id: 139887606
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 7, 'group_counter': 1219, 'group_order': 672, 'label': '2F', 'order': 2, 'powers': [1, 7, 7], 'representative': 9, 'size': 1}
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id: 139887617
{'aut_label': '2B', 'centralizer': '1.a1', 'counter': 8, 'group_counter': 1219, 'group_order': 672, 'label': '2G', 'order': 2, 'powers': [1, 8, 8], 'representative': 345, 'size': 1}
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id: 139887628
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 9, 'group_counter': 1219, 'group_order': 672, 'label': '2H', 'order': 2, 'powers': [1, 9, 9], 'representative': 2, 'size': 3}
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id: 139887304
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 10, 'group_counter': 1219, 'group_order': 672, 'label': '2I', 'order': 2, 'powers': [1, 10, 10], 'representative': 114, 'size': 3}
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id: 139887315
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 11, 'group_counter': 1219, 'group_order': 672, 'label': '2J', 'order': 2, 'powers': [1, 11, 11], 'representative': 10, 'size': 3}
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id: 139887326
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 12, 'group_counter': 1219, 'group_order': 672, 'label': '2K', 'order': 2, 'powers': [1, 12, 12], 'representative': 122, 'size': 3}
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id: 139887337
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 13, 'group_counter': 1219, 'group_order': 672, 'label': '2L', 'order': 2, 'powers': [1, 13, 13], 'representative': 3, 'size': 3}
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id: 139887348
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 14, 'group_counter': 1219, 'group_order': 672, 'label': '2M', 'order': 2, 'powers': [1, 14, 14], 'representative': 115, 'size': 3}
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id: 139887359
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 15, 'group_counter': 1219, 'group_order': 672, 'label': '2N', 'order': 2, 'powers': [1, 15, 15], 'representative': 11, 'size': 3}
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id: 139887370
{'aut_label': '2H', 'centralizer': '3.a1', 'counter': 16, 'group_counter': 1219, 'group_order': 672, 'label': '2O', 'order': 2, 'powers': [1, 16, 16], 'representative': 123, 'size': 3}
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id: 139887381
{'aut_label': '3A', 'centralizer': '2.c1', 'counter': 17, 'group_counter': 1219, 'group_order': 672, 'label': '3A', 'order': 3, 'powers': [17, 1, 17], 'representative': 224, 'size': 2}
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id: 139887392
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 18, 'group_counter': 1219, 'group_order': 672, 'label': '4A1', 'order': 4, 'powers': [2, 19, 19], 'representative': 4, 'size': 1}
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id: 139887403
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 19, 'group_counter': 1219, 'group_order': 672, 'label': '4A-1', 'order': 4, 'powers': [2, 18, 18], 'representative': 12, 'size': 1}
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id: 139887415
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 20, 'group_counter': 1219, 'group_order': 672, 'label': '4B1', 'order': 4, 'powers': [2, 21, 21], 'representative': 340, 'size': 1}
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id: 139887426
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 21, 'group_counter': 1219, 'group_order': 672, 'label': '4B-1', 'order': 4, 'powers': [2, 20, 20], 'representative': 348, 'size': 1}
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id: 139887437
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 22, 'group_counter': 1219, 'group_order': 672, 'label': '4C1', 'order': 4, 'powers': [2, 23, 23], 'representative': 5, 'size': 1}
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id: 139887448
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 23, 'group_counter': 1219, 'group_order': 672, 'label': '4C-1', 'order': 4, 'powers': [2, 22, 22], 'representative': 13, 'size': 1}
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id: 139887459
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 24, 'group_counter': 1219, 'group_order': 672, 'label': '4D1', 'order': 4, 'powers': [2, 25, 25], 'representative': 341, 'size': 1}
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id: 139887470
{'aut_label': '4A1', 'centralizer': '1.a1', 'counter': 25, 'group_counter': 1219, 'group_order': 672, 'label': '4D-1', 'order': 4, 'powers': [2, 24, 24], 'representative': 349, 'size': 1}
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id: 139887481
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 26, 'group_counter': 1219, 'group_order': 672, 'label': '4E1', 'order': 4, 'powers': [2, 27, 27], 'representative': 14, 'size': 3}
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id: 139887492
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 27, 'group_counter': 1219, 'group_order': 672, 'label': '4E-1', 'order': 4, 'powers': [2, 26, 26], 'representative': 6, 'size': 3}
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id: 139887503
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 28, 'group_counter': 1219, 'group_order': 672, 'label': '4F1', 'order': 4, 'powers': [2, 29, 29], 'representative': 126, 'size': 3}
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id: 139887514
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 29, 'group_counter': 1219, 'group_order': 672, 'label': '4F-1', 'order': 4, 'powers': [2, 28, 28], 'representative': 118, 'size': 3}
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id: 139887526
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 30, 'group_counter': 1219, 'group_order': 672, 'label': '4G1', 'order': 4, 'powers': [2, 31, 31], 'representative': 15, 'size': 3}
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id: 139887537
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 31, 'group_counter': 1219, 'group_order': 672, 'label': '4G-1', 'order': 4, 'powers': [2, 30, 30], 'representative': 7, 'size': 3}
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id: 139887548
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 32, 'group_counter': 1219, 'group_order': 672, 'label': '4H1', 'order': 4, 'powers': [2, 33, 33], 'representative': 127, 'size': 3}
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id: 139887559
{'aut_label': '4E1', 'centralizer': '3.a1', 'counter': 33, 'group_counter': 1219, 'group_order': 672, 'label': '4H-1', 'order': 4, 'powers': [2, 32, 32], 'representative': 119, 'size': 3}
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id: 139887567
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 34, 'group_counter': 1219, 'group_order': 672, 'label': '6A', 'order': 6, 'powers': [17, 3, 34], 'representative': 112, 'size': 2}
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id: 139887568
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 35, 'group_counter': 1219, 'group_order': 672, 'label': '6B', 'order': 6, 'powers': [17, 4, 35], 'representative': 120, 'size': 2}
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id: 139887569
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 36, 'group_counter': 1219, 'group_order': 672, 'label': '6C', 'order': 6, 'powers': [17, 5, 36], 'representative': 225, 'size': 2}
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id: 139887570
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 37, 'group_counter': 1219, 'group_order': 672, 'label': '6D', 'order': 6, 'powers': [17, 6, 37], 'representative': 113, 'size': 2}
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id: 139887571
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 38, 'group_counter': 1219, 'group_order': 672, 'label': '6E', 'order': 6, 'powers': [17, 7, 38], 'representative': 233, 'size': 2}
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id: 139887572
{'aut_label': '6A', 'centralizer': '2.c1', 'counter': 39, 'group_counter': 1219, 'group_order': 672, 'label': '6F', 'order': 6, 'powers': [17, 8, 39], 'representative': 121, 'size': 2}
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id: 139887574
{'aut_label': '6G', 'centralizer': '2.c1', 'counter': 40, 'group_counter': 1219, 'group_order': 672, 'label': '6G', 'order': 6, 'powers': [17, 2, 40], 'representative': 456, 'size': 2}
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id: 139887575
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 41, 'group_counter': 1219, 'group_order': 672, 'label': '7A1', 'order': 7, 'powers': [43, 45, 1], 'representative': 192, 'size': 1}
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id: 139887576
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 42, 'group_counter': 1219, 'group_order': 672, 'label': '7A-1', 'order': 7, 'powers': [44, 46, 1], 'representative': 480, 'size': 1}
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id: 139887577
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 43, 'group_counter': 1219, 'group_order': 672, 'label': '7A2', 'order': 7, 'powers': [46, 42, 1], 'representative': 384, 'size': 1}
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id: 139887578
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 44, 'group_counter': 1219, 'group_order': 672, 'label': '7A-2', 'order': 7, 'powers': [45, 41, 1], 'representative': 288, 'size': 1}
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id: 139887579
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 45, 'group_counter': 1219, 'group_order': 672, 'label': '7A3', 'order': 7, 'powers': [42, 43, 1], 'representative': 576, 'size': 1}
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id: 139887580
{'aut_label': '7A1', 'centralizer': '1.a1', 'counter': 46, 'group_counter': 1219, 'group_order': 672, 'label': '7A-3', 'order': 7, 'powers': [41, 44, 1], 'representative': 96, 'size': 1}
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id: 139887581
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 47, 'group_counter': 1219, 'group_order': 672, 'label': '12A1', 'order': 12, 'powers': [40, 18, 48], 'representative': 236, 'size': 2}
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id: 139887582
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 48, 'group_counter': 1219, 'group_order': 672, 'label': '12A-1', 'order': 12, 'powers': [40, 19, 47], 'representative': 452, 'size': 2}
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id: 139887583
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 49, 'group_counter': 1219, 'group_order': 672, 'label': '12B1', 'order': 12, 'powers': [40, 20, 50], 'representative': 124, 'size': 2}
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id: 139887585
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 50, 'group_counter': 1219, 'group_order': 672, 'label': '12B-1', 'order': 12, 'powers': [40, 21, 49], 'representative': 564, 'size': 2}
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id: 139887586
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 51, 'group_counter': 1219, 'group_order': 672, 'label': '12C1', 'order': 12, 'powers': [40, 22, 52], 'representative': 237, 'size': 2}
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id: 139887587
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 52, 'group_counter': 1219, 'group_order': 672, 'label': '12C-1', 'order': 12, 'powers': [40, 23, 51], 'representative': 453, 'size': 2}
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id: 139887588
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 53, 'group_counter': 1219, 'group_order': 672, 'label': '12D1', 'order': 12, 'powers': [40, 24, 54], 'representative': 125, 'size': 2}
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id: 139887589
{'aut_label': '12A1', 'centralizer': '2.c1', 'counter': 54, 'group_counter': 1219, 'group_order': 672, 'label': '12D-1', 'order': 12, 'powers': [40, 25, 53], 'representative': 565, 'size': 2}
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id: 139887590
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 55, 'group_counter': 1219, 'group_order': 672, 'label': '14A1', 'order': 14, 'powers': [43, 57, 2], 'representative': 200, 'size': 1}
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id: 139887591
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 56, 'group_counter': 1219, 'group_order': 672, 'label': '14A-1', 'order': 14, 'powers': [44, 58, 2], 'representative': 488, 'size': 1}
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id: 139887592
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 57, 'group_counter': 1219, 'group_order': 672, 'label': '14A3', 'order': 14, 'powers': [42, 60, 2], 'representative': 584, 'size': 1}
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id: 139887593
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 58, 'group_counter': 1219, 'group_order': 672, 'label': '14A-3', 'order': 14, 'powers': [41, 59, 2], 'representative': 104, 'size': 1}
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id: 139887594
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 59, 'group_counter': 1219, 'group_order': 672, 'label': '14A5', 'order': 14, 'powers': [45, 55, 2], 'representative': 296, 'size': 1}
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id: 139887596
{'aut_label': '14A1', 'centralizer': '1.a1', 'counter': 60, 'group_counter': 1219, 'group_order': 672, 'label': '14A-5', 'order': 14, 'powers': [46, 56, 2], 'representative': 392, 'size': 1}
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id: 139887597
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 61, 'group_counter': 1219, 'group_order': 672, 'label': '14B1', 'order': 14, 'powers': [46, 63, 3], 'representative': 48, 'size': 1}
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id: 139887598
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 62, 'group_counter': 1219, 'group_order': 672, 'label': '14B-1', 'order': 14, 'powers': [45, 64, 3], 'representative': 624, 'size': 1}
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id: 139887599
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 63, 'group_counter': 1219, 'group_order': 672, 'label': '14B3', 'order': 14, 'powers': [44, 66, 3], 'representative': 144, 'size': 1}
-
id: 139887600
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 64, 'group_counter': 1219, 'group_order': 672, 'label': '14B-3', 'order': 14, 'powers': [43, 65, 3], 'representative': 528, 'size': 1}
-
id: 139887601
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 65, 'group_counter': 1219, 'group_order': 672, 'label': '14B5', 'order': 14, 'powers': [42, 61, 3], 'representative': 240, 'size': 1}
-
id: 139887602
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 66, 'group_counter': 1219, 'group_order': 672, 'label': '14B-5', 'order': 14, 'powers': [41, 62, 3], 'representative': 432, 'size': 1}
-
id: 139887603
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 67, 'group_counter': 1219, 'group_order': 672, 'label': '14C1', 'order': 14, 'powers': [46, 69, 4], 'representative': 56, 'size': 1}
-
id: 139887604
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 68, 'group_counter': 1219, 'group_order': 672, 'label': '14C-1', 'order': 14, 'powers': [45, 70, 4], 'representative': 632, 'size': 1}
-
id: 139887605
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 69, 'group_counter': 1219, 'group_order': 672, 'label': '14C3', 'order': 14, 'powers': [44, 72, 4], 'representative': 152, 'size': 1}
-
id: 139887607
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 70, 'group_counter': 1219, 'group_order': 672, 'label': '14C-3', 'order': 14, 'powers': [43, 71, 4], 'representative': 536, 'size': 1}
-
id: 139887608
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 71, 'group_counter': 1219, 'group_order': 672, 'label': '14C5', 'order': 14, 'powers': [42, 67, 4], 'representative': 248, 'size': 1}
-
id: 139887609
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 72, 'group_counter': 1219, 'group_order': 672, 'label': '14C-5', 'order': 14, 'powers': [41, 68, 4], 'representative': 440, 'size': 1}
-
id: 139887610
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 73, 'group_counter': 1219, 'group_order': 672, 'label': '14D1', 'order': 14, 'powers': [41, 75, 5], 'representative': 97, 'size': 1}
-
id: 139887611
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 74, 'group_counter': 1219, 'group_order': 672, 'label': '14D-1', 'order': 14, 'powers': [42, 76, 5], 'representative': 577, 'size': 1}
-
id: 139887612
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 75, 'group_counter': 1219, 'group_order': 672, 'label': '14D3', 'order': 14, 'powers': [45, 78, 5], 'representative': 289, 'size': 1}
-
id: 139887613
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 76, 'group_counter': 1219, 'group_order': 672, 'label': '14D-3', 'order': 14, 'powers': [46, 77, 5], 'representative': 385, 'size': 1}
-
id: 139887614
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 77, 'group_counter': 1219, 'group_order': 672, 'label': '14D5', 'order': 14, 'powers': [44, 73, 5], 'representative': 481, 'size': 1}
-
id: 139887615
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 78, 'group_counter': 1219, 'group_order': 672, 'label': '14D-5', 'order': 14, 'powers': [43, 74, 5], 'representative': 193, 'size': 1}
-
id: 139887616
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 79, 'group_counter': 1219, 'group_order': 672, 'label': '14E1', 'order': 14, 'powers': [46, 81, 6], 'representative': 49, 'size': 1}
-
id: 139887618
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 80, 'group_counter': 1219, 'group_order': 672, 'label': '14E-1', 'order': 14, 'powers': [45, 82, 6], 'representative': 625, 'size': 1}
-
id: 139887619
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 81, 'group_counter': 1219, 'group_order': 672, 'label': '14E3', 'order': 14, 'powers': [44, 84, 6], 'representative': 145, 'size': 1}
-
id: 139887620
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 82, 'group_counter': 1219, 'group_order': 672, 'label': '14E-3', 'order': 14, 'powers': [43, 83, 6], 'representative': 529, 'size': 1}
-
id: 139887621
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 83, 'group_counter': 1219, 'group_order': 672, 'label': '14E5', 'order': 14, 'powers': [42, 79, 6], 'representative': 241, 'size': 1}
-
id: 139887622
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 84, 'group_counter': 1219, 'group_order': 672, 'label': '14E-5', 'order': 14, 'powers': [41, 80, 6], 'representative': 433, 'size': 1}
-
id: 139887623
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 85, 'group_counter': 1219, 'group_order': 672, 'label': '14F1', 'order': 14, 'powers': [41, 87, 7], 'representative': 105, 'size': 1}
-
id: 139887624
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 86, 'group_counter': 1219, 'group_order': 672, 'label': '14F-1', 'order': 14, 'powers': [42, 88, 7], 'representative': 585, 'size': 1}
-
id: 139887625
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 87, 'group_counter': 1219, 'group_order': 672, 'label': '14F3', 'order': 14, 'powers': [45, 90, 7], 'representative': 297, 'size': 1}
-
id: 139887626
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 88, 'group_counter': 1219, 'group_order': 672, 'label': '14F-3', 'order': 14, 'powers': [46, 89, 7], 'representative': 393, 'size': 1}
-
id: 139887627
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 89, 'group_counter': 1219, 'group_order': 672, 'label': '14F5', 'order': 14, 'powers': [44, 85, 7], 'representative': 489, 'size': 1}
-
id: 139887629
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 90, 'group_counter': 1219, 'group_order': 672, 'label': '14F-5', 'order': 14, 'powers': [43, 86, 7], 'representative': 201, 'size': 1}
-
id: 139887630
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 91, 'group_counter': 1219, 'group_order': 672, 'label': '14G1', 'order': 14, 'powers': [46, 93, 8], 'representative': 57, 'size': 1}
-
id: 139887631
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 92, 'group_counter': 1219, 'group_order': 672, 'label': '14G-1', 'order': 14, 'powers': [45, 94, 8], 'representative': 633, 'size': 1}
-
id: 139887632
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 93, 'group_counter': 1219, 'group_order': 672, 'label': '14G3', 'order': 14, 'powers': [44, 96, 8], 'representative': 153, 'size': 1}
-
id: 139887633
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 94, 'group_counter': 1219, 'group_order': 672, 'label': '14G-3', 'order': 14, 'powers': [43, 95, 8], 'representative': 537, 'size': 1}
-
id: 139887634
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 95, 'group_counter': 1219, 'group_order': 672, 'label': '14G5', 'order': 14, 'powers': [42, 91, 8], 'representative': 249, 'size': 1}
-
id: 139887635
{'aut_label': '14B1', 'centralizer': '1.a1', 'counter': 96, 'group_counter': 1219, 'group_order': 672, 'label': '14G-5', 'order': 14, 'powers': [41, 92, 8], 'representative': 441, 'size': 1}
-
id: 139887636
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 97, 'group_counter': 1219, 'group_order': 672, 'label': '14H1', 'order': 14, 'powers': [41, 99, 9], 'representative': 98, 'size': 3}
-
id: 139887637
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 98, 'group_counter': 1219, 'group_order': 672, 'label': '14H-1', 'order': 14, 'powers': [42, 100, 9], 'representative': 578, 'size': 3}
-
id: 139887638
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 99, 'group_counter': 1219, 'group_order': 672, 'label': '14H3', 'order': 14, 'powers': [45, 102, 9], 'representative': 66, 'size': 3}
-
id: 139887305
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 100, 'group_counter': 1219, 'group_order': 672, 'label': '14H-3', 'order': 14, 'powers': [46, 101, 9], 'representative': 386, 'size': 3}
-
id: 139887306
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 101, 'group_counter': 1219, 'group_order': 672, 'label': '14H5', 'order': 14, 'powers': [44, 97, 9], 'representative': 34, 'size': 3}
-
id: 139887307
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 102, 'group_counter': 1219, 'group_order': 672, 'label': '14H-5', 'order': 14, 'powers': [43, 98, 9], 'representative': 194, 'size': 3}
-
id: 139887308
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 103, 'group_counter': 1219, 'group_order': 672, 'label': '14I1', 'order': 14, 'powers': [42, 105, 10], 'representative': 18, 'size': 3}
-
id: 139887309
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 104, 'group_counter': 1219, 'group_order': 672, 'label': '14I-1', 'order': 14, 'powers': [41, 106, 10], 'representative': 210, 'size': 3}
-
id: 139887310
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 105, 'group_counter': 1219, 'group_order': 672, 'label': '14I3', 'order': 14, 'powers': [46, 108, 10], 'representative': 50, 'size': 3}
-
id: 139887311
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 106, 'group_counter': 1219, 'group_order': 672, 'label': '14I-3', 'order': 14, 'powers': [45, 107, 10], 'representative': 402, 'size': 3}
-
id: 139887312
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 107, 'group_counter': 1219, 'group_order': 672, 'label': '14I5', 'order': 14, 'powers': [43, 103, 10], 'representative': 82, 'size': 3}
-
id: 139887313
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 108, 'group_counter': 1219, 'group_order': 672, 'label': '14I-5', 'order': 14, 'powers': [44, 104, 10], 'representative': 594, 'size': 3}
-
id: 139887314
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 109, 'group_counter': 1219, 'group_order': 672, 'label': '14J1', 'order': 14, 'powers': [41, 111, 11], 'representative': 106, 'size': 3}
-
id: 139887316
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 110, 'group_counter': 1219, 'group_order': 672, 'label': '14J-1', 'order': 14, 'powers': [42, 112, 11], 'representative': 586, 'size': 3}
-
id: 139887317
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 111, 'group_counter': 1219, 'group_order': 672, 'label': '14J3', 'order': 14, 'powers': [45, 114, 11], 'representative': 74, 'size': 3}
-
id: 139887318
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 112, 'group_counter': 1219, 'group_order': 672, 'label': '14J-3', 'order': 14, 'powers': [46, 113, 11], 'representative': 394, 'size': 3}
-
id: 139887319
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 113, 'group_counter': 1219, 'group_order': 672, 'label': '14J5', 'order': 14, 'powers': [44, 109, 11], 'representative': 42, 'size': 3}
-
id: 139887320
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 114, 'group_counter': 1219, 'group_order': 672, 'label': '14J-5', 'order': 14, 'powers': [43, 110, 11], 'representative': 202, 'size': 3}
-
id: 139887321
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 115, 'group_counter': 1219, 'group_order': 672, 'label': '14K1', 'order': 14, 'powers': [42, 117, 12], 'representative': 26, 'size': 3}
-
id: 139887322
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 116, 'group_counter': 1219, 'group_order': 672, 'label': '14K-1', 'order': 14, 'powers': [41, 118, 12], 'representative': 218, 'size': 3}
-
id: 139887323
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 117, 'group_counter': 1219, 'group_order': 672, 'label': '14K3', 'order': 14, 'powers': [46, 120, 12], 'representative': 58, 'size': 3}
-
id: 139887324
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 118, 'group_counter': 1219, 'group_order': 672, 'label': '14K-3', 'order': 14, 'powers': [45, 119, 12], 'representative': 410, 'size': 3}
-
id: 139887325
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 119, 'group_counter': 1219, 'group_order': 672, 'label': '14K5', 'order': 14, 'powers': [43, 115, 12], 'representative': 90, 'size': 3}
-
id: 139887327
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 120, 'group_counter': 1219, 'group_order': 672, 'label': '14K-5', 'order': 14, 'powers': [44, 116, 12], 'representative': 602, 'size': 3}
-
id: 139887328
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 121, 'group_counter': 1219, 'group_order': 672, 'label': '14L1', 'order': 14, 'powers': [41, 123, 13], 'representative': 99, 'size': 3}
-
id: 139887329
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 122, 'group_counter': 1219, 'group_order': 672, 'label': '14L-1', 'order': 14, 'powers': [42, 124, 13], 'representative': 579, 'size': 3}
-
id: 139887330
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 123, 'group_counter': 1219, 'group_order': 672, 'label': '14L3', 'order': 14, 'powers': [45, 126, 13], 'representative': 67, 'size': 3}
-
id: 139887331
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 124, 'group_counter': 1219, 'group_order': 672, 'label': '14L-3', 'order': 14, 'powers': [46, 125, 13], 'representative': 387, 'size': 3}
-
id: 139887332
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 125, 'group_counter': 1219, 'group_order': 672, 'label': '14L5', 'order': 14, 'powers': [44, 121, 13], 'representative': 35, 'size': 3}
-
id: 139887333
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 126, 'group_counter': 1219, 'group_order': 672, 'label': '14L-5', 'order': 14, 'powers': [43, 122, 13], 'representative': 195, 'size': 3}
-
id: 139887334
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 127, 'group_counter': 1219, 'group_order': 672, 'label': '14M1', 'order': 14, 'powers': [42, 129, 14], 'representative': 19, 'size': 3}
-
id: 139887335
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 128, 'group_counter': 1219, 'group_order': 672, 'label': '14M-1', 'order': 14, 'powers': [41, 130, 14], 'representative': 211, 'size': 3}
-
id: 139887336
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 129, 'group_counter': 1219, 'group_order': 672, 'label': '14M3', 'order': 14, 'powers': [46, 132, 14], 'representative': 51, 'size': 3}
-
id: 139887338
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 130, 'group_counter': 1219, 'group_order': 672, 'label': '14M-3', 'order': 14, 'powers': [45, 131, 14], 'representative': 403, 'size': 3}
-
id: 139887339
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 131, 'group_counter': 1219, 'group_order': 672, 'label': '14M5', 'order': 14, 'powers': [43, 127, 14], 'representative': 83, 'size': 3}
-
id: 139887340
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 132, 'group_counter': 1219, 'group_order': 672, 'label': '14M-5', 'order': 14, 'powers': [44, 128, 14], 'representative': 595, 'size': 3}
-
id: 139887341
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 133, 'group_counter': 1219, 'group_order': 672, 'label': '14N1', 'order': 14, 'powers': [41, 135, 15], 'representative': 107, 'size': 3}
-
id: 139887342
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 134, 'group_counter': 1219, 'group_order': 672, 'label': '14N-1', 'order': 14, 'powers': [42, 136, 15], 'representative': 587, 'size': 3}
-
id: 139887343
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 135, 'group_counter': 1219, 'group_order': 672, 'label': '14N3', 'order': 14, 'powers': [45, 138, 15], 'representative': 75, 'size': 3}
-
id: 139887344
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 136, 'group_counter': 1219, 'group_order': 672, 'label': '14N-3', 'order': 14, 'powers': [46, 137, 15], 'representative': 395, 'size': 3}
-
id: 139887345
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 137, 'group_counter': 1219, 'group_order': 672, 'label': '14N5', 'order': 14, 'powers': [44, 133, 15], 'representative': 43, 'size': 3}
-
id: 139887346
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 138, 'group_counter': 1219, 'group_order': 672, 'label': '14N-5', 'order': 14, 'powers': [43, 134, 15], 'representative': 203, 'size': 3}
-
id: 139887347
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 139, 'group_counter': 1219, 'group_order': 672, 'label': '14O1', 'order': 14, 'powers': [42, 141, 16], 'representative': 27, 'size': 3}
-
id: 139887349
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 140, 'group_counter': 1219, 'group_order': 672, 'label': '14O-1', 'order': 14, 'powers': [41, 142, 16], 'representative': 219, 'size': 3}
-
id: 139887350
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 141, 'group_counter': 1219, 'group_order': 672, 'label': '14O3', 'order': 14, 'powers': [46, 144, 16], 'representative': 59, 'size': 3}
-
id: 139887351
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 142, 'group_counter': 1219, 'group_order': 672, 'label': '14O-3', 'order': 14, 'powers': [45, 143, 16], 'representative': 411, 'size': 3}
-
id: 139887352
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 143, 'group_counter': 1219, 'group_order': 672, 'label': '14O5', 'order': 14, 'powers': [43, 139, 16], 'representative': 91, 'size': 3}
-
id: 139887353
{'aut_label': '14H1', 'centralizer': '3.a1', 'counter': 144, 'group_counter': 1219, 'group_order': 672, 'label': '14O-5', 'order': 14, 'powers': [44, 140, 16], 'representative': 603, 'size': 3}
-
id: 139887354
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 145, 'group_counter': 1219, 'group_order': 672, 'label': '21A1', 'order': 21, 'powers': [147, 46, 17], 'representative': 32, 'size': 2}
-
id: 139887355
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 146, 'group_counter': 1219, 'group_order': 672, 'label': '21A-1', 'order': 21, 'powers': [148, 45, 17], 'representative': 640, 'size': 2}
-
id: 139887356
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 147, 'group_counter': 1219, 'group_order': 672, 'label': '21A2', 'order': 21, 'powers': [149, 41, 17], 'representative': 64, 'size': 2}
-
id: 139887357
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 148, 'group_counter': 1219, 'group_order': 672, 'label': '21A-2', 'order': 21, 'powers': [150, 42, 17], 'representative': 608, 'size': 2}
-
id: 139887358
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 149, 'group_counter': 1219, 'group_order': 672, 'label': '21A4', 'order': 21, 'powers': [145, 43, 17], 'representative': 128, 'size': 2}
-
id: 139887360
{'aut_label': '21A1', 'centralizer': '2.c1', 'counter': 150, 'group_counter': 1219, 'group_order': 672, 'label': '21A-4', 'order': 21, 'powers': [146, 44, 17], 'representative': 544, 'size': 2}
-
id: 139887361
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 151, 'group_counter': 1219, 'group_order': 672, 'label': '28A1', 'order': 28, 'powers': [55, 153, 18], 'representative': 108, 'size': 1}
-
id: 139887362
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 152, 'group_counter': 1219, 'group_order': 672, 'label': '28A-1', 'order': 28, 'powers': [56, 154, 19], 'representative': 580, 'size': 1}
-
id: 139887363
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 153, 'group_counter': 1219, 'group_order': 672, 'label': '28A3', 'order': 28, 'powers': [57, 157, 19], 'representative': 292, 'size': 1}
-
id: 139887364
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 154, 'group_counter': 1219, 'group_order': 672, 'label': '28A-3', 'order': 28, 'powers': [58, 158, 18], 'representative': 396, 'size': 1}
-
id: 139887365
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 155, 'group_counter': 1219, 'group_order': 672, 'label': '28A5', 'order': 28, 'powers': [59, 162, 18], 'representative': 492, 'size': 1}
-
id: 139887366
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 156, 'group_counter': 1219, 'group_order': 672, 'label': '28A-5', 'order': 28, 'powers': [60, 161, 19], 'representative': 196, 'size': 1}
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id: 139887367
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 157, 'group_counter': 1219, 'group_order': 672, 'label': '28A9', 'order': 28, 'powers': [60, 152, 18], 'representative': 204, 'size': 1}
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id: 139887368
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 158, 'group_counter': 1219, 'group_order': 672, 'label': '28A-9', 'order': 28, 'powers': [59, 151, 19], 'representative': 484, 'size': 1}
-
id: 139887369
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 159, 'group_counter': 1219, 'group_order': 672, 'label': '28A11', 'order': 28, 'powers': [58, 155, 19], 'representative': 388, 'size': 1}
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id: 139887371
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 160, 'group_counter': 1219, 'group_order': 672, 'label': '28A-11', 'order': 28, 'powers': [57, 156, 18], 'representative': 300, 'size': 1}
-
id: 139887372
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 161, 'group_counter': 1219, 'group_order': 672, 'label': '28A13', 'order': 28, 'powers': [56, 159, 18], 'representative': 588, 'size': 1}
-
id: 139887373
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 162, 'group_counter': 1219, 'group_order': 672, 'label': '28A-13', 'order': 28, 'powers': [55, 160, 19], 'representative': 100, 'size': 1}
-
id: 139887374
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 163, 'group_counter': 1219, 'group_order': 672, 'label': '28B1', 'order': 28, 'powers': [58, 165, 20], 'representative': 60, 'size': 1}
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id: 139887375
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 164, 'group_counter': 1219, 'group_order': 672, 'label': '28B-1', 'order': 28, 'powers': [57, 166, 21], 'representative': 628, 'size': 1}
-
id: 139887376
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 165, 'group_counter': 1219, 'group_order': 672, 'label': '28B3', 'order': 28, 'powers': [59, 169, 21], 'representative': 148, 'size': 1}
-
id: 139887377
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 166, 'group_counter': 1219, 'group_order': 672, 'label': '28B-3', 'order': 28, 'powers': [60, 170, 20], 'representative': 540, 'size': 1}
-
id: 139887378
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 167, 'group_counter': 1219, 'group_order': 672, 'label': '28B5', 'order': 28, 'powers': [56, 174, 20], 'representative': 252, 'size': 1}
-
id: 139887379
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 168, 'group_counter': 1219, 'group_order': 672, 'label': '28B-5', 'order': 28, 'powers': [55, 173, 21], 'representative': 436, 'size': 1}
-
id: 139887380
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 169, 'group_counter': 1219, 'group_order': 672, 'label': '28B9', 'order': 28, 'powers': [55, 164, 20], 'representative': 444, 'size': 1}
-
id: 139887382
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 170, 'group_counter': 1219, 'group_order': 672, 'label': '28B-9', 'order': 28, 'powers': [56, 163, 21], 'representative': 244, 'size': 1}
-
id: 139887383
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 171, 'group_counter': 1219, 'group_order': 672, 'label': '28B11', 'order': 28, 'powers': [60, 167, 21], 'representative': 532, 'size': 1}
-
id: 139887384
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 172, 'group_counter': 1219, 'group_order': 672, 'label': '28B-11', 'order': 28, 'powers': [59, 168, 20], 'representative': 156, 'size': 1}
-
id: 139887385
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 173, 'group_counter': 1219, 'group_order': 672, 'label': '28B13', 'order': 28, 'powers': [57, 171, 20], 'representative': 636, 'size': 1}
-
id: 139887386
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 174, 'group_counter': 1219, 'group_order': 672, 'label': '28B-13', 'order': 28, 'powers': [58, 172, 21], 'representative': 52, 'size': 1}
-
id: 139887387
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 175, 'group_counter': 1219, 'group_order': 672, 'label': '28C1', 'order': 28, 'powers': [55, 177, 22], 'representative': 109, 'size': 1}
-
id: 139887388
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 176, 'group_counter': 1219, 'group_order': 672, 'label': '28C-1', 'order': 28, 'powers': [56, 178, 23], 'representative': 581, 'size': 1}
-
id: 139887389
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 177, 'group_counter': 1219, 'group_order': 672, 'label': '28C3', 'order': 28, 'powers': [57, 181, 23], 'representative': 293, 'size': 1}
-
id: 139887390
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 178, 'group_counter': 1219, 'group_order': 672, 'label': '28C-3', 'order': 28, 'powers': [58, 182, 22], 'representative': 397, 'size': 1}
-
id: 139887391
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 179, 'group_counter': 1219, 'group_order': 672, 'label': '28C5', 'order': 28, 'powers': [59, 186, 22], 'representative': 493, 'size': 1}
-
id: 139887393
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 180, 'group_counter': 1219, 'group_order': 672, 'label': '28C-5', 'order': 28, 'powers': [60, 185, 23], 'representative': 197, 'size': 1}
-
id: 139887394
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 181, 'group_counter': 1219, 'group_order': 672, 'label': '28C9', 'order': 28, 'powers': [60, 176, 22], 'representative': 205, 'size': 1}
-
id: 139887395
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 182, 'group_counter': 1219, 'group_order': 672, 'label': '28C-9', 'order': 28, 'powers': [59, 175, 23], 'representative': 485, 'size': 1}
-
id: 139887396
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 183, 'group_counter': 1219, 'group_order': 672, 'label': '28C11', 'order': 28, 'powers': [58, 179, 23], 'representative': 389, 'size': 1}
-
id: 139887397
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 184, 'group_counter': 1219, 'group_order': 672, 'label': '28C-11', 'order': 28, 'powers': [57, 180, 22], 'representative': 301, 'size': 1}
-
id: 139887398
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 185, 'group_counter': 1219, 'group_order': 672, 'label': '28C13', 'order': 28, 'powers': [56, 183, 22], 'representative': 589, 'size': 1}
-
id: 139887399
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 186, 'group_counter': 1219, 'group_order': 672, 'label': '28C-13', 'order': 28, 'powers': [55, 184, 23], 'representative': 101, 'size': 1}
-
id: 139887400
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 187, 'group_counter': 1219, 'group_order': 672, 'label': '28D1', 'order': 28, 'powers': [58, 189, 24], 'representative': 61, 'size': 1}
-
id: 139887401
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 188, 'group_counter': 1219, 'group_order': 672, 'label': '28D-1', 'order': 28, 'powers': [57, 190, 25], 'representative': 629, 'size': 1}
-
id: 139887402
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 189, 'group_counter': 1219, 'group_order': 672, 'label': '28D3', 'order': 28, 'powers': [59, 193, 25], 'representative': 149, 'size': 1}
-
id: 139887404
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 190, 'group_counter': 1219, 'group_order': 672, 'label': '28D-3', 'order': 28, 'powers': [60, 194, 24], 'representative': 541, 'size': 1}
-
id: 139887405
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 191, 'group_counter': 1219, 'group_order': 672, 'label': '28D5', 'order': 28, 'powers': [56, 198, 24], 'representative': 253, 'size': 1}
-
id: 139887406
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 192, 'group_counter': 1219, 'group_order': 672, 'label': '28D-5', 'order': 28, 'powers': [55, 197, 25], 'representative': 437, 'size': 1}
-
id: 139887407
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 193, 'group_counter': 1219, 'group_order': 672, 'label': '28D9', 'order': 28, 'powers': [55, 188, 24], 'representative': 445, 'size': 1}
-
id: 139887408
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 194, 'group_counter': 1219, 'group_order': 672, 'label': '28D-9', 'order': 28, 'powers': [56, 187, 25], 'representative': 245, 'size': 1}
-
id: 139887409
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 195, 'group_counter': 1219, 'group_order': 672, 'label': '28D11', 'order': 28, 'powers': [60, 191, 25], 'representative': 533, 'size': 1}
-
id: 139887410
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 196, 'group_counter': 1219, 'group_order': 672, 'label': '28D-11', 'order': 28, 'powers': [59, 192, 24], 'representative': 157, 'size': 1}
-
id: 139887411
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 197, 'group_counter': 1219, 'group_order': 672, 'label': '28D13', 'order': 28, 'powers': [57, 195, 24], 'representative': 637, 'size': 1}
-
id: 139887412
{'aut_label': '28A1', 'centralizer': '1.a1', 'counter': 198, 'group_counter': 1219, 'group_order': 672, 'label': '28D-13', 'order': 28, 'powers': [58, 196, 25], 'representative': 53, 'size': 1}
-
id: 139887413
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 199, 'group_counter': 1219, 'group_order': 672, 'label': '28E1', 'order': 28, 'powers': [55, 201, 26], 'representative': 102, 'size': 3}
-
id: 139887416
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 200, 'group_counter': 1219, 'group_order': 672, 'label': '28E-1', 'order': 28, 'powers': [56, 202, 27], 'representative': 590, 'size': 3}
-
id: 139887417
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 201, 'group_counter': 1219, 'group_order': 672, 'label': '28E3', 'order': 28, 'powers': [57, 205, 27], 'representative': 78, 'size': 3}
-
id: 139887418
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 202, 'group_counter': 1219, 'group_order': 672, 'label': '28E-3', 'order': 28, 'powers': [58, 206, 26], 'representative': 390, 'size': 3}
-
id: 139887419
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 203, 'group_counter': 1219, 'group_order': 672, 'label': '28E5', 'order': 28, 'powers': [59, 210, 26], 'representative': 38, 'size': 3}
-
id: 139887420
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 204, 'group_counter': 1219, 'group_order': 672, 'label': '28E-5', 'order': 28, 'powers': [60, 209, 27], 'representative': 206, 'size': 3}
-
id: 139887421
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 205, 'group_counter': 1219, 'group_order': 672, 'label': '28E9', 'order': 28, 'powers': [60, 200, 26], 'representative': 198, 'size': 3}
-
id: 139887422
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 206, 'group_counter': 1219, 'group_order': 672, 'label': '28E-9', 'order': 28, 'powers': [59, 199, 27], 'representative': 46, 'size': 3}
-
id: 139887423
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 207, 'group_counter': 1219, 'group_order': 672, 'label': '28E11', 'order': 28, 'powers': [58, 203, 27], 'representative': 398, 'size': 3}
-
id: 139887424
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 208, 'group_counter': 1219, 'group_order': 672, 'label': '28E-11', 'order': 28, 'powers': [57, 204, 26], 'representative': 70, 'size': 3}
-
id: 139887425
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 209, 'group_counter': 1219, 'group_order': 672, 'label': '28E13', 'order': 28, 'powers': [56, 207, 26], 'representative': 582, 'size': 3}
-
id: 139887427
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 210, 'group_counter': 1219, 'group_order': 672, 'label': '28E-13', 'order': 28, 'powers': [55, 208, 27], 'representative': 110, 'size': 3}
-
id: 139887428
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 211, 'group_counter': 1219, 'group_order': 672, 'label': '28F1', 'order': 28, 'powers': [56, 213, 28], 'representative': 22, 'size': 3}
-
id: 139887429
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 212, 'group_counter': 1219, 'group_order': 672, 'label': '28F-1', 'order': 28, 'powers': [55, 214, 29], 'representative': 222, 'size': 3}
-
id: 139887430
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 213, 'group_counter': 1219, 'group_order': 672, 'label': '28F3', 'order': 28, 'powers': [58, 217, 29], 'representative': 62, 'size': 3}
-
id: 139887431
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 214, 'group_counter': 1219, 'group_order': 672, 'label': '28F-3', 'order': 28, 'powers': [57, 218, 28], 'representative': 406, 'size': 3}
-
id: 139887432
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 215, 'group_counter': 1219, 'group_order': 672, 'label': '28F5', 'order': 28, 'powers': [60, 222, 28], 'representative': 86, 'size': 3}
-
id: 139887433
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 216, 'group_counter': 1219, 'group_order': 672, 'label': '28F-5', 'order': 28, 'powers': [59, 221, 29], 'representative': 606, 'size': 3}
-
id: 139887434
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 217, 'group_counter': 1219, 'group_order': 672, 'label': '28F9', 'order': 28, 'powers': [59, 212, 28], 'representative': 598, 'size': 3}
-
id: 139887435
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 218, 'group_counter': 1219, 'group_order': 672, 'label': '28F-9', 'order': 28, 'powers': [60, 211, 29], 'representative': 94, 'size': 3}
-
id: 139887436
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 219, 'group_counter': 1219, 'group_order': 672, 'label': '28F11', 'order': 28, 'powers': [57, 215, 29], 'representative': 414, 'size': 3}
-
id: 139887438
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 220, 'group_counter': 1219, 'group_order': 672, 'label': '28F-11', 'order': 28, 'powers': [58, 216, 28], 'representative': 54, 'size': 3}
-
id: 139887439
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 221, 'group_counter': 1219, 'group_order': 672, 'label': '28F13', 'order': 28, 'powers': [55, 219, 28], 'representative': 214, 'size': 3}
-
id: 139887440
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 222, 'group_counter': 1219, 'group_order': 672, 'label': '28F-13', 'order': 28, 'powers': [56, 220, 29], 'representative': 30, 'size': 3}
-
id: 139887441
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 223, 'group_counter': 1219, 'group_order': 672, 'label': '28G1', 'order': 28, 'powers': [55, 225, 30], 'representative': 103, 'size': 3}
-
id: 139887442
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 224, 'group_counter': 1219, 'group_order': 672, 'label': '28G-1', 'order': 28, 'powers': [56, 226, 31], 'representative': 591, 'size': 3}
-
id: 139887443
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 225, 'group_counter': 1219, 'group_order': 672, 'label': '28G3', 'order': 28, 'powers': [57, 229, 31], 'representative': 79, 'size': 3}
-
id: 139887444
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 226, 'group_counter': 1219, 'group_order': 672, 'label': '28G-3', 'order': 28, 'powers': [58, 230, 30], 'representative': 391, 'size': 3}
-
id: 139887445
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 227, 'group_counter': 1219, 'group_order': 672, 'label': '28G5', 'order': 28, 'powers': [59, 234, 30], 'representative': 39, 'size': 3}
-
id: 139887446
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 228, 'group_counter': 1219, 'group_order': 672, 'label': '28G-5', 'order': 28, 'powers': [60, 233, 31], 'representative': 207, 'size': 3}
-
id: 139887447
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 229, 'group_counter': 1219, 'group_order': 672, 'label': '28G9', 'order': 28, 'powers': [60, 224, 30], 'representative': 199, 'size': 3}
-
id: 139887449
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 230, 'group_counter': 1219, 'group_order': 672, 'label': '28G-9', 'order': 28, 'powers': [59, 223, 31], 'representative': 47, 'size': 3}
-
id: 139887450
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 231, 'group_counter': 1219, 'group_order': 672, 'label': '28G11', 'order': 28, 'powers': [58, 227, 31], 'representative': 399, 'size': 3}
-
id: 139887451
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 232, 'group_counter': 1219, 'group_order': 672, 'label': '28G-11', 'order': 28, 'powers': [57, 228, 30], 'representative': 71, 'size': 3}
-
id: 139887452
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 233, 'group_counter': 1219, 'group_order': 672, 'label': '28G13', 'order': 28, 'powers': [56, 231, 30], 'representative': 583, 'size': 3}
-
id: 139887453
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 234, 'group_counter': 1219, 'group_order': 672, 'label': '28G-13', 'order': 28, 'powers': [55, 232, 31], 'representative': 111, 'size': 3}
-
id: 139887454
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 235, 'group_counter': 1219, 'group_order': 672, 'label': '28H1', 'order': 28, 'powers': [56, 237, 32], 'representative': 23, 'size': 3}
-
id: 139887455
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 236, 'group_counter': 1219, 'group_order': 672, 'label': '28H-1', 'order': 28, 'powers': [55, 238, 33], 'representative': 223, 'size': 3}
-
id: 139887456
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 237, 'group_counter': 1219, 'group_order': 672, 'label': '28H3', 'order': 28, 'powers': [58, 241, 33], 'representative': 63, 'size': 3}
-
id: 139887457
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 238, 'group_counter': 1219, 'group_order': 672, 'label': '28H-3', 'order': 28, 'powers': [57, 242, 32], 'representative': 407, 'size': 3}
-
id: 139887458
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 239, 'group_counter': 1219, 'group_order': 672, 'label': '28H5', 'order': 28, 'powers': [60, 246, 32], 'representative': 87, 'size': 3}
-
id: 139887460
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 240, 'group_counter': 1219, 'group_order': 672, 'label': '28H-5', 'order': 28, 'powers': [59, 245, 33], 'representative': 607, 'size': 3}
-
id: 139887461
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 241, 'group_counter': 1219, 'group_order': 672, 'label': '28H9', 'order': 28, 'powers': [59, 236, 32], 'representative': 599, 'size': 3}
-
id: 139887462
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 242, 'group_counter': 1219, 'group_order': 672, 'label': '28H-9', 'order': 28, 'powers': [60, 235, 33], 'representative': 95, 'size': 3}
-
id: 139887463
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 243, 'group_counter': 1219, 'group_order': 672, 'label': '28H11', 'order': 28, 'powers': [57, 239, 33], 'representative': 415, 'size': 3}
-
id: 139887464
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 244, 'group_counter': 1219, 'group_order': 672, 'label': '28H-11', 'order': 28, 'powers': [58, 240, 32], 'representative': 55, 'size': 3}
-
id: 139887465
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 245, 'group_counter': 1219, 'group_order': 672, 'label': '28H13', 'order': 28, 'powers': [55, 243, 32], 'representative': 215, 'size': 3}
-
id: 139887466
{'aut_label': '28E1', 'centralizer': '3.a1', 'counter': 246, 'group_counter': 1219, 'group_order': 672, 'label': '28H-13', 'order': 28, 'powers': [56, 244, 33], 'representative': 31, 'size': 3}
-
id: 139887467
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 247, 'group_counter': 1219, 'group_order': 672, 'label': '42A1', 'order': 42, 'powers': [145, 61, 34], 'representative': 16, 'size': 2}
-
id: 139887468
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 248, 'group_counter': 1219, 'group_order': 672, 'label': '42A-1', 'order': 42, 'powers': [146, 62, 34], 'representative': 208, 'size': 2}
-
id: 139887469
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 249, 'group_counter': 1219, 'group_order': 672, 'label': '42A5', 'order': 42, 'powers': [148, 65, 34], 'representative': 80, 'size': 2}
-
id: 139887471
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 250, 'group_counter': 1219, 'group_order': 672, 'label': '42A-5', 'order': 42, 'powers': [147, 66, 34], 'representative': 592, 'size': 2}
-
id: 139887472
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 251, 'group_counter': 1219, 'group_order': 672, 'label': '42A11', 'order': 42, 'powers': [149, 64, 34], 'representative': 400, 'size': 2}
-
id: 139887473
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 252, 'group_counter': 1219, 'group_order': 672, 'label': '42A-11', 'order': 42, 'powers': [150, 63, 34], 'representative': 496, 'size': 2}
-
id: 139887474
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 253, 'group_counter': 1219, 'group_order': 672, 'label': '42B1', 'order': 42, 'powers': [145, 67, 35], 'representative': 24, 'size': 2}
-
id: 139887475
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 254, 'group_counter': 1219, 'group_order': 672, 'label': '42B-1', 'order': 42, 'powers': [146, 68, 35], 'representative': 216, 'size': 2}
-
id: 139887476
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 255, 'group_counter': 1219, 'group_order': 672, 'label': '42B5', 'order': 42, 'powers': [148, 71, 35], 'representative': 88, 'size': 2}
-
id: 139887477
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 256, 'group_counter': 1219, 'group_order': 672, 'label': '42B-5', 'order': 42, 'powers': [147, 72, 35], 'representative': 600, 'size': 2}
-
id: 139887478
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 257, 'group_counter': 1219, 'group_order': 672, 'label': '42B11', 'order': 42, 'powers': [149, 70, 35], 'representative': 408, 'size': 2}
-
id: 139887479
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 258, 'group_counter': 1219, 'group_order': 672, 'label': '42B-11', 'order': 42, 'powers': [150, 69, 35], 'representative': 504, 'size': 2}
-
id: 139887480
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 259, 'group_counter': 1219, 'group_order': 672, 'label': '42C1', 'order': 42, 'powers': [147, 73, 36], 'representative': 33, 'size': 2}
-
id: 139887482
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 260, 'group_counter': 1219, 'group_order': 672, 'label': '42C-1', 'order': 42, 'powers': [148, 74, 36], 'representative': 417, 'size': 2}
-
id: 139887483
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 261, 'group_counter': 1219, 'group_order': 672, 'label': '42C5', 'order': 42, 'powers': [150, 77, 36], 'representative': 161, 'size': 2}
-
id: 139887484
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 262, 'group_counter': 1219, 'group_order': 672, 'label': '42C-5', 'order': 42, 'powers': [149, 78, 36], 'representative': 65, 'size': 2}
-
id: 139887485
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 263, 'group_counter': 1219, 'group_order': 672, 'label': '42C11', 'order': 42, 'powers': [145, 76, 36], 'representative': 129, 'size': 2}
-
id: 139887486
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 264, 'group_counter': 1219, 'group_order': 672, 'label': '42C-11', 'order': 42, 'powers': [146, 75, 36], 'representative': 321, 'size': 2}
-
id: 139887487
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 265, 'group_counter': 1219, 'group_order': 672, 'label': '42D1', 'order': 42, 'powers': [145, 79, 37], 'representative': 17, 'size': 2}
-
id: 139887488
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 266, 'group_counter': 1219, 'group_order': 672, 'label': '42D-1', 'order': 42, 'powers': [146, 80, 37], 'representative': 209, 'size': 2}
-
id: 139887489
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 267, 'group_counter': 1219, 'group_order': 672, 'label': '42D5', 'order': 42, 'powers': [148, 83, 37], 'representative': 81, 'size': 2}
-
id: 139887490
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 268, 'group_counter': 1219, 'group_order': 672, 'label': '42D-5', 'order': 42, 'powers': [147, 84, 37], 'representative': 593, 'size': 2}
-
id: 139887491
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 269, 'group_counter': 1219, 'group_order': 672, 'label': '42D11', 'order': 42, 'powers': [149, 82, 37], 'representative': 401, 'size': 2}
-
id: 139887493
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 270, 'group_counter': 1219, 'group_order': 672, 'label': '42D-11', 'order': 42, 'powers': [150, 81, 37], 'representative': 497, 'size': 2}
-
id: 139887494
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 271, 'group_counter': 1219, 'group_order': 672, 'label': '42E1', 'order': 42, 'powers': [147, 85, 38], 'representative': 41, 'size': 2}
-
id: 139887495
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 272, 'group_counter': 1219, 'group_order': 672, 'label': '42E-1', 'order': 42, 'powers': [148, 86, 38], 'representative': 425, 'size': 2}
-
id: 139887496
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 273, 'group_counter': 1219, 'group_order': 672, 'label': '42E5', 'order': 42, 'powers': [150, 89, 38], 'representative': 169, 'size': 2}
-
id: 139887497
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 274, 'group_counter': 1219, 'group_order': 672, 'label': '42E-5', 'order': 42, 'powers': [149, 90, 38], 'representative': 73, 'size': 2}
-
id: 139887498
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 275, 'group_counter': 1219, 'group_order': 672, 'label': '42E11', 'order': 42, 'powers': [145, 88, 38], 'representative': 137, 'size': 2}
-
id: 139887499
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 276, 'group_counter': 1219, 'group_order': 672, 'label': '42E-11', 'order': 42, 'powers': [146, 87, 38], 'representative': 329, 'size': 2}
-
id: 139887500
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 277, 'group_counter': 1219, 'group_order': 672, 'label': '42F1', 'order': 42, 'powers': [145, 91, 39], 'representative': 25, 'size': 2}
-
id: 139887501
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 278, 'group_counter': 1219, 'group_order': 672, 'label': '42F-1', 'order': 42, 'powers': [146, 92, 39], 'representative': 217, 'size': 2}
-
id: 139887502
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 279, 'group_counter': 1219, 'group_order': 672, 'label': '42F5', 'order': 42, 'powers': [148, 95, 39], 'representative': 89, 'size': 2}
-
id: 139887504
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 280, 'group_counter': 1219, 'group_order': 672, 'label': '42F-5', 'order': 42, 'powers': [147, 96, 39], 'representative': 601, 'size': 2}
-
id: 139887505
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 281, 'group_counter': 1219, 'group_order': 672, 'label': '42F11', 'order': 42, 'powers': [149, 94, 39], 'representative': 409, 'size': 2}
-
id: 139887506
{'aut_label': '42A1', 'centralizer': '2.c1', 'counter': 282, 'group_counter': 1219, 'group_order': 672, 'label': '42F-11', 'order': 42, 'powers': [150, 93, 39], 'representative': 505, 'size': 2}
-
id: 139887507
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 283, 'group_counter': 1219, 'group_order': 672, 'label': '42G1', 'order': 42, 'powers': [149, 55, 40], 'representative': 72, 'size': 2}
-
id: 139887508
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 284, 'group_counter': 1219, 'group_order': 672, 'label': '42G-1', 'order': 42, 'powers': [150, 56, 40], 'representative': 616, 'size': 2}
-
id: 139887509
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 285, 'group_counter': 1219, 'group_order': 672, 'label': '42G5', 'order': 42, 'powers': [146, 59, 40], 'representative': 328, 'size': 2}
-
id: 139887510
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 286, 'group_counter': 1219, 'group_order': 672, 'label': '42G-5', 'order': 42, 'powers': [145, 60, 40], 'representative': 360, 'size': 2}
-
id: 139887511
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 287, 'group_counter': 1219, 'group_order': 672, 'label': '42G11', 'order': 42, 'powers': [147, 58, 40], 'representative': 40, 'size': 2}
-
id: 139887512
{'aut_label': '42G1', 'centralizer': '2.c1', 'counter': 288, 'group_counter': 1219, 'group_order': 672, 'label': '42G-11', 'order': 42, 'powers': [148, 57, 40], 'representative': 648, 'size': 2}
-
id: 139887513
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 289, 'group_counter': 1219, 'group_order': 672, 'label': '84A1', 'order': 84, 'powers': [283, 151, 47], 'representative': 36, 'size': 2}
-
id: 139887515
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 290, 'group_counter': 1219, 'group_order': 672, 'label': '84A-1', 'order': 84, 'powers': [284, 152, 48], 'representative': 428, 'size': 2}
-
id: 139887516
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 291, 'group_counter': 1219, 'group_order': 672, 'label': '84A5', 'order': 84, 'powers': [285, 155, 47], 'representative': 164, 'size': 2}
-
id: 139887517
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 292, 'group_counter': 1219, 'group_order': 672, 'label': '84A-5', 'order': 84, 'powers': [286, 156, 48], 'representative': 76, 'size': 2}
-
id: 139887518
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 293, 'group_counter': 1219, 'group_order': 672, 'label': '84A11', 'order': 84, 'powers': [287, 159, 48], 'representative': 140, 'size': 2}
-
id: 139887519
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 294, 'group_counter': 1219, 'group_order': 672, 'label': '84A-11', 'order': 84, 'powers': [288, 160, 47], 'representative': 324, 'size': 2}
-
id: 139887520
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 295, 'group_counter': 1219, 'group_order': 672, 'label': '84A13', 'order': 84, 'powers': [284, 161, 47], 'representative': 420, 'size': 2}
-
id: 139887521
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 296, 'group_counter': 1219, 'group_order': 672, 'label': '84A-13', 'order': 84, 'powers': [283, 162, 48], 'representative': 44, 'size': 2}
-
id: 139887522
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 297, 'group_counter': 1219, 'group_order': 672, 'label': '84A19', 'order': 84, 'powers': [285, 158, 48], 'representative': 172, 'size': 2}
-
id: 139887523
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 298, 'group_counter': 1219, 'group_order': 672, 'label': '84A-19', 'order': 84, 'powers': [286, 157, 47], 'representative': 68, 'size': 2}
-
id: 139887524
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 299, 'group_counter': 1219, 'group_order': 672, 'label': '84A25', 'order': 84, 'powers': [287, 154, 47], 'representative': 132, 'size': 2}
-
id: 139887527
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 300, 'group_counter': 1219, 'group_order': 672, 'label': '84A-25', 'order': 84, 'powers': [288, 153, 48], 'representative': 332, 'size': 2}
-
id: 139887528
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 301, 'group_counter': 1219, 'group_order': 672, 'label': '84B1', 'order': 84, 'powers': [287, 163, 49], 'representative': 20, 'size': 2}
-
id: 139887529
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 302, 'group_counter': 1219, 'group_order': 672, 'label': '84B-1', 'order': 84, 'powers': [288, 164, 50], 'representative': 220, 'size': 2}
-
id: 139887530
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 303, 'group_counter': 1219, 'group_order': 672, 'label': '84B5', 'order': 84, 'powers': [284, 167, 49], 'representative': 84, 'size': 2}
-
id: 139887531
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 304, 'group_counter': 1219, 'group_order': 672, 'label': '84B-5', 'order': 84, 'powers': [283, 168, 50], 'representative': 604, 'size': 2}
-
id: 139887532
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 305, 'group_counter': 1219, 'group_order': 672, 'label': '84B11', 'order': 84, 'powers': [286, 171, 50], 'representative': 412, 'size': 2}
-
id: 139887533
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 306, 'group_counter': 1219, 'group_order': 672, 'label': '84B-11', 'order': 84, 'powers': [285, 172, 49], 'representative': 500, 'size': 2}
-
id: 139887534
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 307, 'group_counter': 1219, 'group_order': 672, 'label': '84B13', 'order': 84, 'powers': [288, 173, 49], 'representative': 212, 'size': 2}
-
id: 139887535
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 308, 'group_counter': 1219, 'group_order': 672, 'label': '84B-13', 'order': 84, 'powers': [287, 174, 50], 'representative': 28, 'size': 2}
-
id: 139887536
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 309, 'group_counter': 1219, 'group_order': 672, 'label': '84B19', 'order': 84, 'powers': [284, 170, 50], 'representative': 92, 'size': 2}
-
id: 139887538
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 310, 'group_counter': 1219, 'group_order': 672, 'label': '84B-19', 'order': 84, 'powers': [283, 169, 49], 'representative': 596, 'size': 2}
-
id: 139887539
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 311, 'group_counter': 1219, 'group_order': 672, 'label': '84B25', 'order': 84, 'powers': [286, 166, 49], 'representative': 404, 'size': 2}
-
id: 139887540
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 312, 'group_counter': 1219, 'group_order': 672, 'label': '84B-25', 'order': 84, 'powers': [285, 165, 50], 'representative': 508, 'size': 2}
-
id: 139887541
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 313, 'group_counter': 1219, 'group_order': 672, 'label': '84C1', 'order': 84, 'powers': [283, 175, 51], 'representative': 37, 'size': 2}
-
id: 139887542
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 314, 'group_counter': 1219, 'group_order': 672, 'label': '84C-1', 'order': 84, 'powers': [284, 176, 52], 'representative': 429, 'size': 2}
-
id: 139887543
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 315, 'group_counter': 1219, 'group_order': 672, 'label': '84C5', 'order': 84, 'powers': [285, 179, 51], 'representative': 165, 'size': 2}
-
id: 139887544
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 316, 'group_counter': 1219, 'group_order': 672, 'label': '84C-5', 'order': 84, 'powers': [286, 180, 52], 'representative': 77, 'size': 2}
-
id: 139887545
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 317, 'group_counter': 1219, 'group_order': 672, 'label': '84C11', 'order': 84, 'powers': [287, 183, 52], 'representative': 141, 'size': 2}
-
id: 139887546
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 318, 'group_counter': 1219, 'group_order': 672, 'label': '84C-11', 'order': 84, 'powers': [288, 184, 51], 'representative': 325, 'size': 2}
-
id: 139887547
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 319, 'group_counter': 1219, 'group_order': 672, 'label': '84C13', 'order': 84, 'powers': [284, 185, 51], 'representative': 421, 'size': 2}
-
id: 139887549
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 320, 'group_counter': 1219, 'group_order': 672, 'label': '84C-13', 'order': 84, 'powers': [283, 186, 52], 'representative': 45, 'size': 2}
-
id: 139887550
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 321, 'group_counter': 1219, 'group_order': 672, 'label': '84C19', 'order': 84, 'powers': [285, 182, 52], 'representative': 173, 'size': 2}
-
id: 139887551
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 322, 'group_counter': 1219, 'group_order': 672, 'label': '84C-19', 'order': 84, 'powers': [286, 181, 51], 'representative': 69, 'size': 2}
-
id: 139887552
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 323, 'group_counter': 1219, 'group_order': 672, 'label': '84C25', 'order': 84, 'powers': [287, 178, 51], 'representative': 133, 'size': 2}
-
id: 139887553
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 324, 'group_counter': 1219, 'group_order': 672, 'label': '84C-25', 'order': 84, 'powers': [288, 177, 52], 'representative': 333, 'size': 2}
-
id: 139887554
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 325, 'group_counter': 1219, 'group_order': 672, 'label': '84D1', 'order': 84, 'powers': [287, 187, 53], 'representative': 21, 'size': 2}
-
id: 139887555
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 326, 'group_counter': 1219, 'group_order': 672, 'label': '84D-1', 'order': 84, 'powers': [288, 188, 54], 'representative': 221, 'size': 2}
-
id: 139887556
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 327, 'group_counter': 1219, 'group_order': 672, 'label': '84D5', 'order': 84, 'powers': [284, 191, 53], 'representative': 85, 'size': 2}
-
id: 139887557
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 328, 'group_counter': 1219, 'group_order': 672, 'label': '84D-5', 'order': 84, 'powers': [283, 192, 54], 'representative': 605, 'size': 2}
-
id: 139887558
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 329, 'group_counter': 1219, 'group_order': 672, 'label': '84D11', 'order': 84, 'powers': [286, 195, 54], 'representative': 413, 'size': 2}
-
id: 139887560
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 330, 'group_counter': 1219, 'group_order': 672, 'label': '84D-11', 'order': 84, 'powers': [285, 196, 53], 'representative': 501, 'size': 2}
-
id: 139887561
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 331, 'group_counter': 1219, 'group_order': 672, 'label': '84D13', 'order': 84, 'powers': [288, 197, 53], 'representative': 213, 'size': 2}
-
id: 139887562
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 332, 'group_counter': 1219, 'group_order': 672, 'label': '84D-13', 'order': 84, 'powers': [287, 198, 54], 'representative': 29, 'size': 2}
-
id: 139887563
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 333, 'group_counter': 1219, 'group_order': 672, 'label': '84D19', 'order': 84, 'powers': [284, 194, 54], 'representative': 93, 'size': 2}
-
id: 139887564
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 334, 'group_counter': 1219, 'group_order': 672, 'label': '84D-19', 'order': 84, 'powers': [283, 193, 53], 'representative': 597, 'size': 2}
-
id: 139887565
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 335, 'group_counter': 1219, 'group_order': 672, 'label': '84D25', 'order': 84, 'powers': [286, 190, 53], 'representative': 405, 'size': 2}
-
id: 139887566
{'aut_label': '84A1', 'centralizer': '2.c1', 'counter': 336, 'group_counter': 1219, 'group_order': 672, 'label': '84D-25', 'order': 84, 'powers': [285, 189, 54], 'representative': 509, 'size': 2}
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gps_qchar • Show schema
Hide schema
-
id: 12800526
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id: 12800537
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id: 12800570
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id: 12800581
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id: 12800592
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id: 12800596
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id: 12800597
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id: 12800527
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id: 12800528
{'cdim': 1, 'counter': 11, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1k', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -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: 12800529
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id: 12800530
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id: 12800531
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id: 12800532
{'cdim': 1, 'counter': 15, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1o', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12800533
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id: 12800534
{'cdim': 1, 'counter': 17, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1q', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, -2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800535
{'cdim': 1, 'counter': 18, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1r', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, -2, 2, -2, 2, 2, -2, -2, 2, 2, 2, 2, 2, 2, 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, 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800536
{'cdim': 1, 'counter': 19, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1s', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, -2, 2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 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, -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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800538
{'cdim': 1, 'counter': 20, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1t', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, -2, 2, 2, -2, -2, 2, -2, 2, 2, 2, 2, 2, 2, 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, -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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800539
{'cdim': 1, 'counter': 21, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1u', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, 2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 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, 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800540
{'cdim': 1, 'counter': 22, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1v', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, 2, -2, -2, -2, 2, 2, -2, 2, 2, 2, 2, 2, 2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800541
{'cdim': 1, 'counter': 23, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1w', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, 2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 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, -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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800542
{'cdim': 1, 'counter': 24, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1x', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [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, 2, -2, 2, 2, -2, -2, -2, 2, 2, 2, 2, 2, 2, 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, -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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800569
{'cdim': 2, 'counter': 49, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, -1, -1, -1, -1, -1, 2, 2, 2, 2, 2, 2, -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, 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, -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, 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, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12800571
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id: 12800572
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id: 12800573
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id: 12800574
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id: 12800575
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id: 12800576
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id: 12800577
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id: 12800578
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id: 12800579
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id: 12800582
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id: 12800546
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id: 12800560
{'cdim': 1, 'counter': 40, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1an', 'multiplicity': 6, 'nt': [14, 1], 'qdim': 6, 'qvalues': [6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, -6, 6, 6, 6, 6, 6, 6, 6, -1, -1, -1, -1, -1, -1, -6, -6, -6, -6, -6, -6, -6, -6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12800561
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id: 12800562
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id: 12800563
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id: 12800564
{'cdim': 1, 'counter': 44, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1ar', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, -12, 12, 12, -12, -12, -12, 12, 12, -12, -12, 12, 12, -12, -12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -12, 12, 12, -12, -12, 12, -12, -2, -2, -2, -2, -2, -2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800565
{'cdim': 1, 'counter': 45, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1as', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, 12, -12, -12, -12, -12, 12, 12, -12, -12, -12, -12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, -12, -12, 12, 12, -12, -2, -2, -2, -2, -2, -2, 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, -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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800566
{'cdim': 1, 'counter': 46, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1at', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, 12, -12, -12, -12, -12, 12, 12, 12, 12, 12, 12, -12, -12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, -12, -12, 12, 12, -12, -2, -2, -2, -2, -2, -2, 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, -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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, -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], 'schur_index': 1}
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id: 12800567
{'cdim': 1, 'counter': 47, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1au', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, 12, -12, -12, -12, -12, 12, 12, -12, -12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 12, 12, -12, -12, -12, -2, -2, -2, -2, -2, -2, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800568
{'cdim': 1, 'counter': 48, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.1av', 'multiplicity': 12, 'nt': [28, 1], 'qdim': 12, 'qvalues': [12, 12, 12, -12, -12, 12, -12, -12, 12, 12, -12, -12, 12, 12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, -12, 12, 12, -12, -12, -12, -2, -2, -2, -2, -2, -2, 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, 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, -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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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], 'schur_index': 1}
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id: 12800583
{'cdim': 2, 'counter': 61, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2m', 'multiplicity': 6, 'nt': [21, 6], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -2, -2, -2, -2, -2, -2, -6, -6, -6, -6, -6, -6, -6, -6, -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, -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, 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, -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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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: 12800584
{'cdim': 2, 'counter': 62, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2n', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, -12, -12, -12, 12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, -12, -12, 12, -12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -6, 6, -6, -6, -2, -2, -2, -2, -2, -2, 6, -6, 6, -6, -6, 6, -6, 6, 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, 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, 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, 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, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, 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: 12800585
{'cdim': 2, 'counter': 63, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2o', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, -12, -12, -12, 12, 12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, 12, 12, -12, 12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, 6, -6, 6, -6, -6, -2, -2, -2, -2, -2, -2, -6, 6, -6, 6, 6, -6, 6, -6, 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, 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, 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, -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, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -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: 12800586
{'cdim': 2, 'counter': 64, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2p', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 12, -12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, -12, 12, -12, 12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -6, 6, -6, 6, -6, -2, -2, -2, -2, -2, -2, -6, -6, 6, 6, -6, -6, 6, 6, -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, -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, 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, 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, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -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: 12800587
{'cdim': 2, 'counter': 65, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2q', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, -12, 12, -12, 12, -12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, 12, -12, 12, -12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, 6, 6, -6, 6, -6, 6, -6, -2, -2, -2, -2, -2, -2, 6, 6, -6, -6, 6, 6, -6, -6, -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, -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, 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, -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, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 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: 12800588
{'cdim': 2, 'counter': 66, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2r', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, 12, -12, 12, 12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, -12, 12, 12, 12, -12, -12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, -6, -2, -2, -2, -2, -2, -2, -6, 6, 6, -6, 6, -6, -6, 6, 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, 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, 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, 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, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, 1, 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: 12800589
{'cdim': 2, 'counter': 67, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2s', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, 12, -12, 12, 12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, 12, 12, -12, -12, -12, 12, 12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, 6, 6, 6, 6, -6, -2, -2, -2, -2, -2, -2, 6, -6, -6, 6, -6, 6, 6, -6, 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, 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, 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, -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, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -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: 12800590
{'cdim': 2, 'counter': 68, 'faithful': False, 'group': '672.1219', 'group_order': 672, 'image': None, 'label': '672.1219.2t', 'multiplicity': 6, 'nt': [42, 12], 'qdim': 12, 'qvalues': [12, 12, 12, 12, 12, 12, 12, 12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -12, -12, -12, -12, -12, -12, -12, -12, 0, 0, 0, 0, 0, 0, 0, 0, -6, -6, -6, -6, -6, -6, -6, -2, -2, -2, -2, -2, -2, 6, 6, 6, 6, 6, 6, 6, 6, -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, -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, 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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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: 12800591
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id: 12800593
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id: 12800594
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id: 12800595
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gps_char • Show schema
Hide schema
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id: 29605667
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id: 29605944
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id: 29605945
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id: 29605946
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id: 29605947
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id: 29605949
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id: 29605950
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id: 29605951
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id: 29605952
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id: 29605953
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id: 29605954
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id: 29605955
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id: 29605956
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id: 29605957
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id: 29605958
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id: 29605960
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id: 29605961
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id: 29605962
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id: 29605963
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id: 29605964
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id: 29605965
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id: 29605966
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id: 29605967
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id: 29605968
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id: 29605969
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id: 29605971
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id: 29605972
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id: 29605973
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id: 29605974
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id: 29605975
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id: 29605976
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id: 29605977
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id: 29605978
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id: 29605979
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id: 29605980
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id: 29605982
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id: 29605983
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id: 29605984
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id: 29605985
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id: 29605986
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id: 29605987
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id: 29605988
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id: 29605989
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id: 29605990
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id: 29605991
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id: 29605993
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id: 29605994
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id: 29605995
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id: 29605996
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id: 29605997
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id: 29605998
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id: 29605999
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id: 29606000
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id: 29606001
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id: 29606002
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id: 29605669
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id: 29605670
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id: 29605671
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id: 29605672
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id: 29605673
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id: 29605674
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id: 29605675
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id: 29605676
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id: 29605677
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id: 29605678
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id: 29605680
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id: 29605681
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id: 29605682
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id: 29605683
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id: 29605684
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id: 29605685
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id: 29605686
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id: 29605687
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id: 29605688
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id: 29605689
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id: 29605691
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id: 29605692
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id: 29605693
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id: 29605694
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id: 29605695
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id: 29605696
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id: 29605697
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id: 29605698
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id: 29605699
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id: 29605700
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id: 29605710
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id: 29605711
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id: 29605713
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id: 29605702
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id: 29605703
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id: 29605704
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id: 29605705
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id: 29605706
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id: 29605707
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id: 29605708
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id: 29605709
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id: 29605714
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id: 29605724
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id: 29605725
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id: 29605726
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id: 29605715
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id: 29605716
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id: 29605717
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id: 29605718
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id: 29605719
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id: 29605720
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id: 29605721
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id: 29605722
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id: 29605727
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id: 29605737
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id: 29605738
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id: 29605739
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id: 29605728
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id: 29605729
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id: 29605730
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id: 29605731
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id: 29605732
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id: 29605733
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id: 29605735
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id: 29605736
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id: 29605740
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id: 29605750
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id: 29605751
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id: 29605752
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id: 29605741
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id: 29605742
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id: 29605743
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id: 29605744
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id: 29605746
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id: 29605747
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id: 29605748
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id: 29605749
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id: 29605753
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id: 29605763
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id: 29605764
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id: 29605765
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id: 29605754
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id: 29605755
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id: 29605757
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id: 29605758
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id: 29605759
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id: 29605760
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id: 29605761
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id: 29605762
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id: 29605766
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id: 29605776
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id: 29605777
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id: 29605780
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id: 29605768
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id: 29605769
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id: 29605770
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id: 29605771
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id: 29605772
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id: 29605773
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id: 29605774
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id: 29605775
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id: 29605781
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id: 29605791
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id: 29605792
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id: 29605793
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id: 29605782
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id: 29605783
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id: 29605784
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id: 29605785
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id: 29605786
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id: 29605787
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id: 29605788
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id: 29605789
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id: 29605794
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id: 29605804
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id: 29605805
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id: 29605806
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id: 29605795
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id: 29605796
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id: 29605797
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id: 29605798
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id: 29605799
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id: 29605800
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id: 29605802
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id: 29605803
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id: 29605778
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id: 29605889
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id: 29605948
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id: 29605959
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id: 29605970
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id: 29605981
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id: 29605992
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id: 29605668
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id: 29605679
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id: 29605690
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id: 29605701
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id: 29605712
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id: 29605723
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id: 29605745
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id: 29605756
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id: 29605790
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id: 29605801
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id: 29605812
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id: 29605823
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id: 29605834
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id: 29605845
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id: 29605856
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id: 29605867
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id: 29605878
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id: 29605890
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id: 29605901
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id: 29605912
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id: 29605923
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id: 29605931
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id: 29605932
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id: 29605933
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id: 29605934
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id: 29605935
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id: 29605936
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id: 29605938
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id: 29605939
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id: 29605940
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id: 29605941
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id: 29605942
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id: 29605807
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id: 29605808
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id: 29605809
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id: 29605810
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id: 29605811
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id: 29605813
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id: 29605814
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id: 29605815
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id: 29605816
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id: 29605817
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id: 29605818
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id: 29605819
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id: 29605820
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id: 29605821
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id: 29605822
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id: 29605824
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id: 29605825
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id: 29605826
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id: 29605827
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id: 29605828
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id: 29605829
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id: 29605830
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id: 29605831
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id: 29605832
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id: 29605833
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id: 29605835
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id: 29605836
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id: 29605837
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id: 29605838
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id: 29605839
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id: 29605840
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id: 29605841
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id: 29605842
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id: 29605843
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id: 29605844
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id: 29605846
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id: 29605847
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id: 29605848
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id: 29605849
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id: 29605850
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id: 29605851
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id: 29605852
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id: 29605853
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id: 29605854
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id: 29605855
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id: 29605857
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id: 29605858
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id: 29605859
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id: 29605860
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id: 29605861
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id: 29605862
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id: 29605863
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id: 29605864
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id: 29605865
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id: 29605866
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id: 29605868
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id: 29605869
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id: 29605870
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id: 29605871
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id: 29605872
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id: 29605873
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id: 29605874
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id: 29605875
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id: 29605876
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id: 29605877
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id: 29605887
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id: 29605888
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id: 29605891
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id: 29605879
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id: 29605880
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id: 29605881
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id: 29605882
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id: 29605883
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id: 29605884
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id: 29605885
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id: 29605886
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id: 29605892
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id: 29605902
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id: 29605903
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id: 29605904
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id: 29605893
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id: 29605894
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id: 29605895
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id: 29605896
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id: 29605897
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id: 29605898
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id: 29605899
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id: 29605900
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id: 29605905
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id: 29605915
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id: 29605916
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id: 29605917
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id: 29605906
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id: 29605907
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id: 29605908
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id: 29605909
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id: 29605910
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id: 29605911
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id: 29605913
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id: 29605914
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id: 29605918
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id: 29605928
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id: 29605929
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id: 29605930
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id: 29605919
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id: 29605920
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id: 29605921
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id: 29605922
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id: 29605924
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id: 29605925
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id: 29605926
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id: 29605927
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-
id: 110439033
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 112, 'characteristic': True, 'core_order': 672, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 42, 'label': '672.1219.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1219', 'subgroup_hash': 1219, 'subgroup_order': 672, 'subgroup_tex': 'C_{84}:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439044
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 336, 'counter': 2, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.185', 'subgroup_hash': 185, 'subgroup_order': 336, 'subgroup_tex': 'D_6\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439055
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': True, 'core_order': 336, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '336.226', 'subgroup_hash': 226, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439066
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 336, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.204', 'subgroup_hash': 204, 'subgroup_order': 336, 'subgroup_tex': 'C_2^2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 110439077
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': True, 'core_order': 336, 'counter': 5, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.2.d1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '336.192', 'subgroup_hash': 192, 'subgroup_order': 336, 'subgroup_tex': 'C_{42}.C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439088
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 112, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 14, 'label': '672.1219.3.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '224.189', 'subgroup_hash': 189, 'subgroup_order': 224, 'subgroup_tex': 'C_2^3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439099
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 168, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['C2'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.55', 'subgroup_hash': 55, 'subgroup_order': 168, 'subgroup_tex': 'D_6\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439110
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 168, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.4.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.39', 'subgroup_hash': 39, 'subgroup_order': 168, 'subgroup_tex': 'C_2\\times C_{84}', 'supersolvable': True, 'sylow': 0}
-
id: 110439116
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 168, 'counter': 9, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.4.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.32', 'subgroup_hash': 32, 'subgroup_order': 168, 'subgroup_tex': 'C_6:C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439034
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 168, 'counter': 10, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.4.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': ['S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '168.57', 'subgroup_hash': 57, 'subgroup_order': 168, 'subgroup_tex': 'C_2^2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 110439035
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 168, 'counter': 11, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.4.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.30', 'subgroup_hash': 30, 'subgroup_order': 168, 'subgroup_tex': 'S_3\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439036
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 168, 'counter': 12, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.4.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.f1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '168.55', 'subgroup_hash': 55, 'subgroup_order': 168, 'subgroup_tex': 'D_6\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439037
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 112, 'counter': 13, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.6.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439038
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 56, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.6.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439039
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 56, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.6.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.43', 'subgroup_hash': 43, 'subgroup_order': 112, 'subgroup_tex': 'C_2^3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439040
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 56, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.6.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '112.37', 'subgroup_hash': 37, 'subgroup_order': 112, 'subgroup_tex': 'C_2^2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439041
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': True, 'core_order': 96, 'counter': 17, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '672.1219.7.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '7.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '7.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 7, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '96.206', 'subgroup_hash': 206, 'subgroup_order': 96, 'subgroup_tex': 'C_{12}:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439042
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 84, 'counter': 18, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.8.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 110439043
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 84, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.8.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439045
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 84, 'counter': 20, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.8.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.6', 'subgroup_hash': 6, 'subgroup_order': 84, 'subgroup_tex': 'C_{84}', 'supersolvable': True, 'sylow': 0}
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id: 110439046
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 84, 'counter': 21, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.8.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.3', 'subgroup_hash': 3, 'subgroup_order': 84, 'subgroup_tex': 'C_3:C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439047
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 84, 'counter': 22, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.13', 'subgroup_hash': 13, 'subgroup_order': 84, 'subgroup_tex': 'S_3\\times C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 110439048
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 84, 'counter': 23, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.8.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.f1', 'outer_equivalence': True, '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '84.15', 'subgroup_hash': 15, 'subgroup_order': 84, 'subgroup_tex': 'C_2\\times C_{42}', 'supersolvable': True, 'sylow': 0}
-
id: 110439049
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 56, 'counter': 24, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
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id: 110439050
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 56, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.12.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '12.4', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 110439051
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.12.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 110439052
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.12.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
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id: 110439053
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.12.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.8', 'subgroup_hash': 8, 'subgroup_order': 56, 'subgroup_tex': 'C_2\\times C_{28}', 'supersolvable': True, 'sylow': 0}
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id: 110439054
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 28, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.12.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '56.13', 'subgroup_hash': 13, 'subgroup_order': 56, 'subgroup_tex': 'C_2^2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
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id: 110439056
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 48, 'counter': 30, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.14.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.35', 'subgroup_hash': 35, 'subgroup_order': 48, 'subgroup_tex': 'C_4\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 110439057
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': True, 'core_order': 48, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.14.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '48.51', 'subgroup_hash': 51, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times D_6', 'supersolvable': True, 'sylow': 0}
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id: 110439058
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 48, 'counter': 32, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.14.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '14.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.44', 'subgroup_hash': 44, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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id: 110439059
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': True, 'core_order': 48, 'counter': 33, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.14.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '14.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '14.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 14, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '48.42', 'subgroup_hash': 42, 'subgroup_order': 48, 'subgroup_tex': 'C_6.C_2^3', 'supersolvable': True, 'sylow': 0}
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id: 110439060
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 42, 'counter': 34, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.16.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.14', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 110439061
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 42, 'counter': 35, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.16.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.6', 'subgroup_hash': 6, 'subgroup_order': 42, 'subgroup_tex': 'C_{42}', 'supersolvable': True, 'sylow': 0}
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id: 110439062
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 42, 'counter': 36, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.16.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '16.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.10', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 10, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '42.3', 'subgroup_hash': 3, 'subgroup_order': 42, 'subgroup_tex': 'S_3\\times C_7', 'supersolvable': True, 'sylow': 0}
-
id: 110439063
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '672.1219.21.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '21.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 21, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.45', 'subgroup_hash': 45, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3\\times C_4', 'supersolvable': True, 'sylow': 2}
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id: 110439064
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 28, 'counter': 38, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.24.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439065
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 28, 'counter': 39, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '672.1219.24.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.14', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 14, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439067
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 28, 'counter': 40, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.24.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '24.5', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times S_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439068
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.24.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439069
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 42, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1219.24.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.2', 'subgroup_hash': 2, 'subgroup_order': 28, 'subgroup_tex': 'C_{28}', 'supersolvable': True, 'sylow': 0}
-
id: 110439070
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 14, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.24.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '28.4', 'subgroup_hash': 4, 'subgroup_order': 28, 'subgroup_tex': 'C_2\\times C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439071
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 44, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.28.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439072
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 24, 'counter': 45, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.28.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110439073
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 46, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.28.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.7', 'subgroup_hash': 7, 'subgroup_order': 24, 'subgroup_tex': 'C_6:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439074
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 24, 'counter': 47, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.28.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '28.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.15', 'subgroup_hash': 15, 'subgroup_order': 24, 'subgroup_tex': 'C_2^2\\times C_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439075
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 48, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.28.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.4', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.5', 'subgroup_hash': 5, 'subgroup_order': 24, 'subgroup_tex': 'C_4\\times S_3', 'supersolvable': True, 'sylow': 0}
-
id: 110439076
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 24, 'counter': 49, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.28.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '28.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '28.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 28, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '24.14', 'subgroup_hash': 14, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times D_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439078
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 21, 'counter': 50, 'cyclic': True, 'direct': False, 'hall': 21, 'label': '672.1219.32.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '32.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '32.45', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 45, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_4', 'simple': False, 'solvable': True, 'special_labels': ['C5'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '21.2', 'subgroup_hash': 2, 'subgroup_order': 21, 'subgroup_tex': 'C_{21}', 'supersolvable': True, 'sylow': 0}
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id: 110439079
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.42.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '42.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '42.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 42, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_7', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439080
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 8, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.42.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439081
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 8, 'counter': 53, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.42.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 110439082
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 8, 'counter': 54, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.42.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '42.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 42, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439083
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 14, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.48.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439084
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 14, 'counter': 56, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '672.1219.48.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.35', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 35, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439085
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 7, 'counter': 57, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1219.48.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '14.2', 'subgroup_hash': 2, 'subgroup_order': 14, 'subgroup_tex': 'C_{14}', 'supersolvable': True, 'sylow': 0}
-
id: 110439086
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 58, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.56.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.13', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, '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: 110439087
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 12, 'counter': 59, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.56.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.13', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439089
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 60, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.56.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.13', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.2', 'subgroup_hash': 2, 'subgroup_order': 12, 'subgroup_tex': 'C_{12}', 'supersolvable': True, 'sylow': 0}
-
id: 110439090
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 12, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.56.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.13', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439091
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 12, 'counter': 62, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.56.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '56.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '12.4', 'subgroup_hash': 4, 'subgroup_order': 12, 'subgroup_tex': 'D_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439092
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 12, 'counter': 63, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.56.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '56.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '56.8', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 8, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 56, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, '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: 110439093
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.84.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439094
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.84.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '84.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '84.13', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 13, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 84, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439095
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.84.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439096
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.84.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439097
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.84.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439098
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 4, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.84.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '84.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 84, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 110439100
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 7, 'counter': 70, 'cyclic': True, 'direct': True, 'hall': 7, 'label': '672.1219.96.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '96.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '96.206', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 206, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['C6'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '7.1', 'subgroup_hash': 1, 'subgroup_order': 7, 'subgroup_tex': 'C_7', 'supersolvable': True, 'sylow': 7}
-
id: 110439101
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 6, 'counter': 71, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.112.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.43', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 43, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 110439102
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': False, 'core_order': 6, 'counter': 72, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.112.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '112.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], '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: 110439103
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': True, 'centralizer_order': 112, 'characteristic': False, 'core_order': 6, 'counter': 73, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.112.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '112.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '112.37', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 37, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 112, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '6.1', 'subgroup_hash': 1, 'subgroup_order': 6, 'subgroup_tex': 'S_3', 'supersolvable': True, 'sylow': 0}
-
id: 110439104
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 4, 'counter': 74, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '672.1219.168.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.55', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 55, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 110439105
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 4, 'counter': 75, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '672.1219.168.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.55', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 55, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{14}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 110439106
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 4, 'counter': 76, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '672.1219.168.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '168.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '168.30', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 168, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3\\times C_{28}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 110439107
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.168.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 110439108
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 78, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1219.168.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
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id: 110439109
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 2, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '672.1219.168.f1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '168.f1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 168, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
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id: 110439111
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 336, 'characteristic': True, 'core_order': 3, 'counter': 80, 'cyclic': True, 'direct': False, 'hall': 3, 'label': '672.1219.224.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '224.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '224.189', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 189, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{28}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
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id: 110439112
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 2, 'counter': 81, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.1219.336.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.226', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 226, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{42}:C_2^3', 'simple': True, 'solvable': True, 'special_labels': ['Phi'], 'split': False, '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: 110439113
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 2, 'counter': 82, 'cyclic': True, 'direct': True, 'hall': 0, 'label': '672.1219.336.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.185', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 185, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_6\\times C_{28}', '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: 110439114
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 224, 'characteristic': False, 'core_order': 1, 'counter': 83, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '672.1219.336.c1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '336.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 336, '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: 110439115
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.1219', 'ambient_counter': 1219, 'ambient_order': 672, 'ambient_tex': 'C_{84}:C_2^3', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': True, 'core_order': 1, 'counter': 84, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '672.1219.672.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '672.a1', 'outer_equivalence': True, 'perfect': True, 'proper': False, 'quotient': '672.1219', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1219, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 672, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{84}:C_2^3', 'simple': False, 'solvable': True, 'special_labels': ['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: 110439033
{'ambient': '672.1219', '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': '6.a1', 'complements': ['672.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '2.c1', '2.d1', '3.a1', '7.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6076, 4057, 5235, 5411], 'generators': [1, 8, 4, 336, 2, 224, 96], 'label': '672.1219.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '2.c1', '2.d1', '7.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 110439034
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '4.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '288.1033', 'aut_weyl_index': 192, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '2.c1', '2.d1'], 'contains': ['8.a1', '8.f1', '12.b1', '28.d1'], 'core': '4.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8630, 5984, 2931, 3736], 'generators': [1, 336, 224, 8, 96], 'label': '672.1219.4.d1', 'mobius_quo': -8, 'mobius_sub': 2, 'normal_closure': '4.d1', 'normal_contained_in': ['2.b1', '2.c1', '2.d1'], 'normal_contains': ['8.a1', '8.f1', '12.b1', '28.d1'], 'normalizer': '1.a1', 'old_label': '4.d1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110439035
{'ambient': '672.1219', 'aut_centralizer_order': 24, 'aut_label': '4.e1', 'aut_quo_index': 1, 'aut_stab_index': 16, 'aut_weyl_group': '144.195', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': ['168.c1', '168.f1'], 'conjugacy_class_count': 16, 'contained_in': ['2.a1'], 'contains': ['8.b1', '8.c1', '8.d1', '12.e1', '28.e1'], 'core': '4.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [411, 4057, 9046, 7022], 'generators': [2, 96, 8, 340, 224], 'label': '672.1219.4.e1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.e1', 'normal_contained_in': ['2.a1'], 'normal_contains': ['8.b1', '8.c1', '8.d1', '28.e1'], 'normalizer': '1.a1', 'old_label': '4.e1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 110439036
{'ambient': '672.1219', 'aut_centralizer_order': 8, 'aut_label': '4.f1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '864.4690', 'aut_weyl_index': 64, 'centralizer': '6.a1', 'complements': ['168.b1', '168.e1'], 'conjugacy_class_count': 8, 'contained_in': ['2.b1'], 'contains': ['8.e1', '8.f1', '12.f1', '28.f1'], 'core': '4.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [9412, 9333, 1220, 1061], 'generators': [1, 336, 96, 2, 224], 'label': '672.1219.4.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': ['2.b1'], 'normal_contains': ['8.e1', '8.f1', '28.f1'], 'normalizer': '1.a1', 'old_label': '4.f1', 'projective_image': '24.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '4.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 110439037
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157766', 'aut_weyl_index': 48, 'centralizer': '1.a1', 'complements': ['112.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '3.a1'], 'contains': ['12.a1', '12.b1', '42.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4257, 435, 5715, 9259], 'generators': [1, 336, 96, 4, 8], 'label': '672.1219.6.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1', 'normal_contained_in': ['2.c1'], 'normal_contains': ['12.a1', '12.b1', '42.a1'], 'normalizer': '1.a1', 'old_label': '6.a1', 'projective_image': '6.1', 'quotient_action_image': '1.1', 'quotient_action_kernel': '6.1', 'quotient_action_kernel_order': 6, 'quotient_fusion': None, 'short_label': '6.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110439038
{'ambient': '672.1219', 'aut_centralizer_order': 8, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '192.1410', 'aut_weyl_index': 288, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '3.a1'], 'contains': ['12.a1', '12.c1', '12.d1', '12.e1', '42.b1'], 'core': '12.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3012, -1, 7359, -1], 'generators': [1, 348, 96, 2, 8], 'label': '672.1219.6.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.b1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110439039
{'ambient': '672.1219', 'aut_centralizer_order': 16, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.157766', 'aut_weyl_index': 48, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '3.a1'], 'contains': ['12.b1', '12.c1', '12.f1', '42.c1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8263, -1, 1936, -1], 'generators': [1, 8, 336, 2, 96], 'label': '672.1219.6.c1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.c1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110439040
{'ambient': '672.1219', 'aut_centralizer_order': 16, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1152.157766', 'aut_weyl_index': 48, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '3.a1'], 'contains': ['12.b1', '12.d1', '42.d1'], 'core': '12.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6558, -1, 4165, -1], 'generators': [1, 336, 96, 6, 8], 'label': '672.1219.6.d1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '6.d1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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id: 110439041
{'ambient': '672.1219', 'aut_centralizer_order': 6, 'aut_label': '7.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '9216.mt', 'aut_weyl_index': 6, 'centralizer': '6.a1', 'complements': ['96.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['14.a1', '14.b1', '14.c1', '14.d1', '21.a1'], 'core': '7.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6188, 3061, 5540, 5411], 'generators': [1, 224, 8, 2, 4, 336], 'label': '672.1219.7.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '7.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['14.a1', '14.b1', '14.c1', '14.d1'], 'normalizer': '1.a1', 'old_label': '7.a1', 'projective_image': '42.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '7.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 110439042
{'ambient': '672.1219', 'aut_centralizer_order': 768, 'aut_label': '8.a1', 'aut_quo_index': 42, 'aut_stab_index': 3, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2304, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'contains': ['16.a1', '16.b1', '24.a1', '56.a1'], 'core': '8.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4643, 5969, 4396, 4424], 'generators': [8, 224, 96, 336], 'label': '672.1219.8.a1', 'mobius_quo': 2, 'mobius_sub': -8, 'normal_closure': '8.a1', 'normal_contained_in': ['4.a1', '4.b1', '4.c1', '4.d1'], 'normal_contains': ['16.a1', '16.b1', '24.a1', '56.a1'], 'normalizer': '1.a1', 'old_label': '8.a1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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id: 110439043
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '8.b1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '72.48', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['4.a1', '4.e1'], 'contains': ['16.a1', '16.c1', '24.d1', '56.b1'], 'core': '8.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [2379, 7024, 4873, 3049], 'generators': [2, 96, 224, 8], 'label': '672.1219.8.b1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.b1', 'normal_contained_in': ['4.a1', '4.e1'], 'normal_contains': ['16.a1', '16.c1', '56.b1'], 'normalizer': '1.a1', 'old_label': '8.b1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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id: 110439044
{'ambient': '672.1219', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '1152.134251', 'aut_weyl_index': 48, 'centralizer': '6.a1', 'complements': ['336.b1', '336.c1'], 'conjugacy_class_count': 12, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.e1', '6.b1', '14.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3012, 4057, 7359, 6416], 'generators': [1, 224, 340, 96, 2, 8], 'label': '672.1219.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.e1', '14.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439045
{'ambient': '672.1219', 'aut_centralizer_order': 576, 'aut_label': '8.c1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2304, 'centralizer': '2.c1', 'complements': ['84.f1'], 'conjugacy_class_count': 4, 'contained_in': ['4.b1', '4.e1'], 'contains': ['16.a1', '24.b1', '56.c1'], 'core': '8.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [130, 2147, 9898, 8473], 'generators': [340, 96, 8, 224], 'label': '672.1219.8.c1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.c1', 'normal_contained_in': ['4.b1', '4.e1'], 'normal_contains': ['16.a1', '24.b1', '56.c1'], 'normalizer': '1.a1', 'old_label': '8.c1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439046
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '8.d1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '72.48', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': ['84.f1'], 'conjugacy_class_count': 4, 'contained_in': ['4.c1', '4.e1'], 'contains': ['16.a1', '24.e1', '56.d1'], 'core': '8.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [1067, 5103, 8652, 6644], 'generators': [6, 8, 224, 96], 'label': '672.1219.8.d1', 'mobius_quo': 0, 'mobius_sub': -8, 'normal_closure': '8.d1', 'normal_contained_in': ['4.c1', '4.e1'], 'normal_contains': ['16.a1', '56.d1'], 'normalizer': '1.a1', 'old_label': '8.d1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.2', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439047
{'ambient': '672.1219', 'aut_centralizer_order': 32, 'aut_label': '8.e1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '72.48', 'aut_weyl_index': 768, 'centralizer': '6.a1', 'complements': ['84.a1', '84.e1', '84.d1'], 'conjugacy_class_count': 24, 'contained_in': ['4.a1', '4.f1'], 'contains': ['16.b1', '16.c1', '24.f1', '56.e1'], 'core': '8.e1', 'coset_action_label': None, 'count': 24, 'diagramx': [7340, 9333, 1685, 979], 'generators': [2, 96, 224, 336], 'label': '672.1219.8.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1', '4.f1'], 'normal_contains': ['16.b1', '16.c1', '56.e1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': '48.35', 'quotient_action_image': '1.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439048
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '8.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '72.48', 'aut_weyl_index': 768, 'centralizer': '2.c1', 'complements': ['84.e1'], 'conjugacy_class_count': 4, 'contained_in': ['4.d1', '4.f1'], 'contains': ['16.b1', '24.c1', '56.f1'], 'core': '8.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [9660, 8079, 752, 1679], 'generators': [1, 224, 96, 336], 'label': '672.1219.8.f1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '8.f1', 'normal_contained_in': ['4.d1', '4.f1'], 'normal_contains': ['16.b1', '24.c1', '56.f1'], 'normalizer': '1.a1', 'old_label': '8.f1', 'projective_image': '24.5', 'quotient_action_image': '2.1', 'quotient_action_kernel': '4.1', 'quotient_action_kernel_order': 4, 'quotient_fusion': None, 'short_label': '8.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439049
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1152, 'centralizer': '1.a1', 'complements': ['56.e1'], 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '6.a1', '6.b1'], 'contains': ['24.a1', '24.b1', '84.a1'], 'core': '12.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1775, 488, 7692, 9689], 'generators': [1, 96, 8, 348], 'label': '672.1219.12.a1', 'mobius_quo': 0, 'mobius_sub': -6, 'normal_closure': '12.a1', 'normal_contained_in': ['4.b1', '6.a1'], 'normal_contains': ['24.a1', '24.b1', '84.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439050
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '12.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '144.188', 'aut_weyl_index': 384, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '6.a1', '6.c1', '6.d1'], 'contains': ['24.a1', '24.c1', '84.b1'], 'core': '12.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8519, 2641, 2431, 5171], 'generators': [1, 336, 96, 8], 'label': '672.1219.12.b1', 'mobius_quo': 8, 'mobius_sub': -6, 'normal_closure': '12.b1', 'normal_contained_in': ['4.d1', '6.a1'], 'normal_contains': ['24.a1', '24.c1', '84.b1'], 'normalizer': '1.a1', 'old_label': '12.b1', 'projective_image': '12.4', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.4', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439051
{'ambient': '672.1219', 'aut_centralizer_order': 64, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1152, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '6.b1', '6.c1'], 'contains': ['24.a1', '24.d1', '24.f1', '84.c1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5854, -1, 3431, -1], 'generators': [2, 336, 96, 8], 'label': '672.1219.12.c1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.c1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439052
{'ambient': '672.1219', 'aut_centralizer_order': 64, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '48.45', 'aut_weyl_index': 1152, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '6.b1', '6.d1'], 'contains': ['24.a1', '24.e1', '84.d1'], 'core': '24.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3753, -1, 6268, -1], 'generators': [6, 96, 8, 336], 'label': '672.1219.12.d1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.d1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439053
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '24.15', 'aut_weyl_index': 2304, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['4.e1', '6.b1'], 'contains': ['24.b1', '24.d1', '24.e1', '84.e1'], 'core': '24.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [411, -1, 9134, -1], 'generators': [2, 96, 8, 348], 'label': '672.1219.12.e1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '4.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.e1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439054
{'ambient': '672.1219', 'aut_centralizer_order': 16, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '144.188', 'aut_weyl_index': 384, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '6.c1'], 'contains': ['24.c1', '24.f1', '84.f1'], 'core': '24.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [9341, -1, 243, -1], 'generators': [1, 336, 96, 2], 'label': '672.1219.12.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '12.f1', 'projective_image': '24.5', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439055
{'ambient': '672.1219', 'aut_centralizer_order': 8, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.d1', '4.f1', '6.c1', '14.b1'], 'core': '2.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8356, 7291, 2682, 2830], 'generators': [1, 224, 8, 336, 2, 96], 'label': '672.1219.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.d1', '4.f1', '14.b1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '12.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439056
{'ambient': '672.1219', 'aut_centralizer_order': 24, 'aut_label': '14.a1', 'aut_quo_index': 1, 'aut_stab_index': 12, 'aut_weyl_group': '192.1147', 'aut_weyl_index': 288, 'centralizer': '6.a1', 'complements': ['48.b1', '48.c1'], 'conjugacy_class_count': 12, 'contained_in': ['2.a1', '7.a1'], 'contains': ['28.a1', '28.b1', '28.c1', '28.e1', '42.b1'], 'core': '14.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3079, 3370, 7935, 6223], 'generators': [1, 224, 2, 348, 8], 'label': '672.1219.14.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.a1', 'normal_contained_in': ['2.a1', '7.a1'], 'normal_contains': ['28.a1', '28.b1', '28.c1', '28.e1'], 'normalizer': '1.a1', 'old_label': '14.a1', 'projective_image': '84.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '14.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439057
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '14.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157664', 'aut_weyl_index': 48, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.b1', '7.a1'], 'contains': ['28.a1', '28.d1', '28.f1', '42.c1'], 'core': '14.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8752, 7659, 2434, 1984], 'generators': [1, 224, 2, 8, 336], 'label': '672.1219.14.b1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.b1', 'normal_contained_in': ['2.b1', '7.a1'], 'normal_contains': ['28.a1', '28.d1', '28.f1'], 'normalizer': '1.a1', 'old_label': '14.b1', 'projective_image': '84.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '14.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439058
{'ambient': '672.1219', 'aut_centralizer_order': 144, 'aut_label': '14.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '384.20089', 'aut_weyl_index': 144, 'centralizer': '2.c1', 'complements': ['48.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.c1', '7.a1'], 'contains': ['28.b1', '28.d1', '42.a1'], 'core': '14.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [5010, 1539, 6253, 7765], 'generators': [1, 8, 4, 336, 224], 'label': '672.1219.14.c1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.c1', 'normal_contained_in': ['2.c1', '7.a1'], 'normal_contains': ['28.b1', '28.d1', '42.a1'], 'normalizer': '1.a1', 'old_label': '14.c1', 'projective_image': '42.3', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439059
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '14.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1152.157664', 'aut_weyl_index': 48, 'centralizer': '6.a1', 'complements': ['48.c1'], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '7.a1'], 'contains': ['28.c1', '28.d1', '42.d1'], 'core': '14.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [7106, 5412, 4709, 4535], 'generators': [1, 224, 6, 336, 8], 'label': '672.1219.14.d1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '14.d1', 'normal_contained_in': ['2.d1', '7.a1'], 'normal_contains': ['28.c1', '28.d1'], 'normalizer': '1.a1', 'old_label': '14.d1', 'projective_image': '84.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '7.1', 'quotient_action_kernel_order': 7, 'quotient_fusion': None, 'short_label': '14.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439060
{'ambient': '672.1219', 'aut_centralizer_order': 4608, 'aut_label': '16.a1', 'aut_quo_index': 210, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'contains': ['32.a1', '48.a1', '112.a1'], 'core': '16.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1260, 6421, 5598, 4857], 'generators': [8, 96, 224], 'label': '672.1219.16.a1', 'mobius_quo': -1, 'mobius_sub': 64, 'normal_closure': '16.a1', 'normal_contained_in': ['8.a1', '8.b1', '8.c1', '8.d1'], 'normal_contains': ['32.a1', '48.a1', '112.a1'], 'normalizer': '1.a1', 'old_label': '16.a1', 'projective_image': '48.51', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.5', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439061
{'ambient': '672.1219', 'aut_centralizer_order': 768, 'aut_label': '16.b1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '2.c1', 'complements': ['42.b1'], 'conjugacy_class_count': 6, 'contained_in': ['8.a1', '8.e1', '8.f1'], 'contains': ['32.a1', '48.b1', '112.b1'], 'core': '16.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7484, 8609, 2685, 2882], 'generators': [336, 96, 224], 'label': '672.1219.16.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '16.b1', 'normal_contained_in': ['8.a1', '8.e1', '8.f1'], 'normal_contains': ['32.a1', '48.b1', '112.b1'], 'normalizer': '1.a1', 'old_label': '16.b1', 'projective_image': '48.35', 'quotient_action_image': '2.1', 'quotient_action_kernel': '8.2', 'quotient_action_kernel_order': 8, 'quotient_fusion': None, 'short_label': '16.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439062
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '16.c1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1536, 'centralizer': '6.a1', 'complements': ['42.a1', '42.b1', '42.d1'], 'conjugacy_class_count': 8, 'contained_in': ['8.b1', '8.e1'], 'contains': ['32.a1', '48.c1', '112.c1'], 'core': '16.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4365, 9397, 3223, 1817], 'generators': [2, 224, 96], 'label': '672.1219.16.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': ['8.b1', '8.e1'], 'normal_contains': ['32.a1', '112.c1'], 'normalizer': '1.a1', 'old_label': '16.c1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '16.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439063
{'ambient': '672.1219', 'aut_centralizer_order': 12, 'aut_label': '21.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1536.408640869', 'aut_weyl_index': 36, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1', '7.a1'], 'contains': ['42.a1', '42.b1', '42.c1', '42.d1'], 'core': '42.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6317, -1, 5215, -1], 'generators': [1, 2, 4, 336], 'label': '672.1219.21.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '7.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '21.a1', 'projective_image': '42.3', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '21.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439064
{'ambient': '672.1219', 'aut_centralizer_order': 1536, 'aut_label': '24.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '12.a1', '12.b1', '12.c1', '12.d1'], 'contains': ['48.a1', '48.b1', '168.a1'], 'core': '24.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5202, 2467, 4142, 5750], 'generators': [8, 96, 336], 'label': '672.1219.24.a1', 'mobius_quo': -2, 'mobius_sub': 24, 'normal_closure': '24.a1', 'normal_contained_in': ['8.a1', '12.a1', '12.b1'], 'normal_contains': ['48.a1', '48.b1', '168.a1'], 'normalizer': '1.a1', 'old_label': '24.a1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439065
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '1.a1', 'complements': ['28.f1'], 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '12.a1', '12.e1'], 'contains': ['48.a1', '168.b1'], 'core': '24.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [181, 556, 7915, 8456], 'generators': [348, 8, 96], 'label': '672.1219.24.b1', 'mobius_quo': 0, 'mobius_sub': 24, 'normal_closure': '24.b1', 'normal_contained_in': ['8.c1', '12.a1'], 'normal_contains': ['48.a1', '168.b1'], 'normalizer': '1.a1', 'old_label': '24.b1', 'projective_image': '24.14', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.14', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439066
{'ambient': '672.1219', 'aut_centralizer_order': 24, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '2304.mr', 'aut_weyl_index': 24, 'centralizer': '2.c1', 'complements': ['336.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.d1', '6.a1', '14.c1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [4576, 2147, 6148, 7765], 'generators': [1, 8, 336, 224, 4, 96], 'label': '672.1219.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.d1', '6.a1', '14.c1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '6.1', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439067
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '24.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '36.12', 'aut_weyl_index': 1536, 'centralizer': '1.a1', 'complements': ['28.e1'], 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '12.b1', '12.f1'], 'contains': ['48.b1', '168.c1'], 'core': '24.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9493, 5523, 1199, 3423], 'generators': [1, 96, 336], 'label': '672.1219.24.c1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '24.c1', 'normal_contained_in': ['8.f1', '12.b1'], 'normal_contains': ['48.b1', '168.c1'], 'normalizer': '1.a1', 'old_label': '24.c1', 'projective_image': '24.5', 'quotient_action_image': '1.1', 'quotient_action_kernel': '24.5', 'quotient_action_kernel_order': 24, 'quotient_fusion': None, 'short_label': '24.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439068
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '12.c1', '12.e1'], 'contains': ['48.a1', '48.c1', '168.d1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2290, -1, 5019, -1], 'generators': [2, 96, 8], 'label': '672.1219.24.d1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.d1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439069
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '12.d1', '12.e1'], 'contains': ['48.a1', '168.e1'], 'core': '48.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [696, -1, 6990, -1], 'generators': [6, 8, 96], 'label': '672.1219.24.e1', 'mobius_quo': None, 'mobius_sub': 8, 'normal_closure': '8.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.e1', 'projective_image': '48.51', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439070
{'ambient': '672.1219', 'aut_centralizer_order': 64, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['8.e1', '12.c1', '12.f1'], 'contains': ['48.b1', '48.c1', '168.f1'], 'core': '48.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [8040, -1, 2316, -1], 'generators': [2, 96, 336], 'label': '672.1219.24.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '8.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '24.f1', 'projective_image': '48.35', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439071
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '28.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['4.a1', '14.a1', '14.b1'], 'contains': ['56.a1', '56.b1', '56.e1', '84.c1'], 'core': '28.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5973, 7434, 3928, 2366], 'generators': [2, 8, 336, 224], 'label': '672.1219.28.a1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '28.a1', 'normal_contained_in': ['4.a1', '14.a1', '14.b1'], 'normal_contains': ['56.a1', '56.b1', '56.e1'], 'normalizer': '1.a1', 'old_label': '28.a1', 'projective_image': '168.55', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '28.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439072
{'ambient': '672.1219', 'aut_centralizer_order': 576, 'aut_label': '28.b1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 3456, 'centralizer': '2.c1', 'complements': ['24.f1'], 'conjugacy_class_count': 6, 'contained_in': ['4.b1', '14.a1', '14.c1'], 'contains': ['56.a1', '56.c1', '84.a1'], 'core': '28.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [2430, 1785, 8169, 7932], 'generators': [1, 348, 224, 8], 'label': '672.1219.28.b1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '28.b1', 'normal_contained_in': ['4.b1', '14.a1', '14.c1'], 'normal_contains': ['56.a1', '56.c1', '84.a1'], 'normalizer': '1.a1', 'old_label': '28.b1', 'projective_image': '84.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439073
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '28.c1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '48.38', 'aut_weyl_index': 1152, 'centralizer': '6.a1', 'complements': ['24.f1'], 'conjugacy_class_count': 6, 'contained_in': ['4.c1', '14.a1', '14.d1'], 'contains': ['56.a1', '56.d1', '84.d1'], 'core': '28.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3605, 4362, 6751, 5927], 'generators': [6, 336, 8, 224], 'label': '672.1219.28.c1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '28.c1', 'normal_contained_in': ['4.c1', '14.a1', '14.d1'], 'normal_contains': ['56.a1', '56.d1'], 'normalizer': '1.a1', 'old_label': '28.c1', 'projective_image': '168.55', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439074
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '28.d1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 1152, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['4.d1', '14.b1', '14.c1', '14.d1'], 'contains': ['56.a1', '56.f1', '84.b1'], 'core': '28.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [8474, 6210, 2931, 3736], 'generators': [1, 8, 336, 224], 'label': '672.1219.28.d1', 'mobius_quo': 8, 'mobius_sub': -2, 'normal_closure': '28.d1', 'normal_contained_in': ['4.d1', '14.b1', '14.c1', '14.d1'], 'normal_contains': ['56.a1', '56.f1', '84.b1'], 'normalizer': '1.a1', 'old_label': '28.d1', 'projective_image': '84.13', 'quotient_action_image': '2.1', 'quotient_action_kernel': '14.2', 'quotient_action_kernel_order': 14, 'quotient_fusion': None, 'short_label': '28.d1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439075
{'ambient': '672.1219', 'aut_centralizer_order': 144, 'aut_label': '28.e1', 'aut_quo_index': 1, 'aut_stab_index': 16, 'aut_weyl_group': '24.14', 'aut_weyl_index': 2304, 'centralizer': '6.a1', 'complements': ['24.c1', '24.f1'], 'conjugacy_class_count': 16, 'contained_in': ['4.e1', '14.a1'], 'contains': ['56.b1', '56.c1', '56.d1', '84.e1'], 'core': '28.e1', 'coset_action_label': None, 'count': 16, 'diagramx': [748, 3370, 9570, 7292], 'generators': [2, 348, 8, 224], 'label': '672.1219.28.e1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '28.e1', 'normal_contained_in': ['4.e1', '14.a1'], 'normal_contains': ['56.b1', '56.c1', '56.d1'], 'normalizer': '1.a1', 'old_label': '28.e1', 'projective_image': '168.55', 'quotient_action_image': '1.1', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '28.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439076
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '28.f1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '144.183', 'aut_weyl_index': 384, 'centralizer': '6.a1', 'complements': ['24.b1', '24.e1'], 'conjugacy_class_count': 8, 'contained_in': ['4.f1', '14.b1'], 'contains': ['56.e1', '56.f1', '84.f1'], 'core': '28.f1', 'coset_action_label': None, 'count': 8, 'diagramx': [9759, 9450, 1220, 296], 'generators': [1, 2, 336, 224], 'label': '672.1219.28.f1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '28.f1', 'normal_contained_in': ['4.f1', '14.b1'], 'normal_contains': ['56.e1', '56.f1'], 'normalizer': '1.a1', 'old_label': '28.f1', 'projective_image': '168.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '28.2', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '28.f1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439077
{'ambient': '672.1219', 'aut_centralizer_order': 8, 'aut_label': '2.d1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '6.a1', 'complements': ['336.c1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.c1', '4.d1', '6.d1', '14.d1'], 'core': '2.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [6718, 5649, 4267, 4338], 'generators': [1, 224, 336, 96, 6, 8], 'label': '672.1219.2.d1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.d1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.c1', '4.d1', '14.d1'], 'normalizer': '1.a1', 'old_label': '2.d1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439078
{'ambient': '672.1219', 'aut_centralizer_order': 4608, 'aut_label': '32.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '12.5', 'aut_weyl_index': 4608, 'centralizer': '2.c1', 'complements': ['21.a1'], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '16.b1', '16.c1'], 'contains': ['96.a1', '224.a1'], 'core': '32.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4431, 8389, 3481, 3144], 'generators': [224, 96], 'label': '672.1219.32.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '32.a1', 'normal_contained_in': ['16.a1', '16.b1', '16.c1'], 'normal_contains': ['96.a1', '224.a1'], 'normalizer': '1.a1', 'old_label': '32.a1', 'projective_image': '96.206', 'quotient_action_image': '2.1', 'quotient_action_kernel': '16.10', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '32.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439079
{'ambient': '672.1219', 'aut_centralizer_order': 288, 'aut_label': '42.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 288, 'centralizer': '1.a1', 'complements': ['16.c1'], 'conjugacy_class_count': 1, 'contained_in': ['6.a1', '14.c1', '21.a1'], 'contains': ['84.a1', '84.b1'], 'core': '42.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5310, 1002, 5800, 9002], 'generators': [1, 4, 336], 'label': '672.1219.42.a1', 'mobius_quo': 0, 'mobius_sub': -3, 'normal_closure': '42.a1', 'normal_contained_in': ['6.a1', '14.c1'], 'normal_contains': ['84.a1', '84.b1'], 'normalizer': '1.a1', 'old_label': '42.a1', 'projective_image': '42.3', 'quotient_action_image': '1.1', 'quotient_action_kernel': '42.3', 'quotient_action_kernel_order': 42, 'quotient_fusion': None, 'short_label': '42.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439080
{'ambient': '672.1219', 'aut_centralizer_order': 48, 'aut_label': '42.b1', 'aut_quo_index': None, 'aut_stab_index': 36, 'aut_weyl_group': '32.27', 'aut_weyl_index': 1728, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 12, 'contained_in': ['6.b1', '14.a1', '21.a1'], 'contains': ['84.a1', '84.c1', '84.d1', '84.e1'], 'core': '84.a1', 'coset_action_label': None, 'count': 36, 'diagramx': [3027, -1, 7224, -1], 'generators': [1, 2, 340], 'label': '672.1219.42.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '14.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '42.b1', 'projective_image': '84.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439081
{'ambient': '672.1219', 'aut_centralizer_order': 96, 'aut_label': '42.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 288, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1', '14.b1', '21.a1'], 'contains': ['84.b1', '84.c1', '84.f1'], 'core': '84.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [8311, -1, 2042, -1], 'generators': [1, 2, 8, 336], 'label': '672.1219.42.c1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '14.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '42.c1', 'projective_image': '84.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439082
{'ambient': '672.1219', 'aut_centralizer_order': 96, 'aut_label': '42.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '192.1493', 'aut_weyl_index': 288, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1', '14.d1', '21.a1'], 'contains': ['84.b1', '84.d1'], 'core': '84.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6739, -1, 5341, -1], 'generators': [1, 6, 336], 'label': '672.1219.42.d1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '14.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '42.d1', 'projective_image': '84.13', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '42.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439083
{'ambient': '672.1219', 'aut_centralizer_order': 9216, 'aut_label': '48.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '24.a1', '24.b1', '24.d1', '24.e1'], 'contains': ['96.a1', '336.a1'], 'core': '48.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1634, 2846, 5268, 5570], 'generators': [8, 96], 'label': '672.1219.48.a1', 'mobius_quo': 1, 'mobius_sub': -192, 'normal_closure': '48.a1', 'normal_contained_in': ['16.a1', '24.a1', '24.b1'], 'normal_contains': ['96.a1', '336.a1'], 'normalizer': '1.a1', 'old_label': '48.a1', 'projective_image': '48.51', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.51', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439084
{'ambient': '672.1219', 'aut_centralizer_order': 1536, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '6.2', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': ['14.a1'], 'conjugacy_class_count': 6, 'contained_in': ['16.b1', '24.a1', '24.c1', '24.f1'], 'contains': ['96.a1', '336.b1'], 'core': '48.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7455, 5150, 2515, 3874], 'generators': [336, 96], 'label': '672.1219.48.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '48.b1', 'normal_contained_in': ['16.b1', '24.a1', '24.c1'], 'normal_contains': ['96.a1', '336.b1'], 'normalizer': '1.a1', 'old_label': '48.b1', 'projective_image': '48.35', 'quotient_action_image': '1.1', 'quotient_action_kernel': '48.35', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '48.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439085
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '6.2', 'aut_weyl_index': 9216, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['16.c1', '24.d1', '24.f1'], 'contains': ['96.a1', '336.c1'], 'core': '96.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5417, -1, 3223, -1], 'generators': [2, 96], 'label': '672.1219.48.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '16.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '48.c1', 'projective_image': '96.206', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439086
{'ambient': '672.1219', 'aut_centralizer_order': 4608, 'aut_label': '56.a1', 'aut_quo_index': 42, 'aut_stab_index': 3, 'aut_weyl_group': '4.2', 'aut_weyl_index': 13824, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['8.a1', '28.a1', '28.b1', '28.c1', '28.d1'], 'contains': ['112.a1', '112.b1', '168.a1'], 'core': '56.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4735, 6095, 4580, 4376], 'generators': [8, 336, 224], 'label': '672.1219.56.a1', 'mobius_quo': -2, 'mobius_sub': 8, 'normal_closure': '56.a1', 'normal_contained_in': ['8.a1', '28.a1', '28.b1', '28.c1', '28.d1'], 'normal_contains': ['112.a1', '112.b1', '168.a1'], 'normalizer': '1.a1', 'old_label': '56.a1', 'projective_image': '168.55', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439087
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '56.b1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 4, 'contained_in': ['8.b1', '28.a1', '28.e1'], 'contains': ['112.a1', '112.c1', '168.d1'], 'core': '56.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1993, 7875, 5364, 3929], 'generators': [2, 8, 224], 'label': '672.1219.56.b1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '56.b1', 'normal_contained_in': ['8.b1', '28.a1', '28.e1'], 'normal_contains': ['112.a1', '112.c1'], 'normalizer': '1.a1', 'old_label': '56.b1', 'projective_image': '336.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '56.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439088
{'ambient': '672.1219', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['6.a1', '6.b1', '6.c1', '6.d1', '21.a1'], 'core': '6.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5735, -1, 4931, -1], 'generators': [1, 8, 4, 336, 2, 96], 'label': '672.1219.3.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '3.a1', 'projective_image': '6.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439089
{'ambient': '672.1219', 'aut_centralizer_order': 3456, 'aut_label': '56.c1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '4.2', 'aut_weyl_index': 13824, 'centralizer': '2.c1', 'complements': ['12.f1'], 'conjugacy_class_count': 4, 'contained_in': ['8.c1', '28.b1', '28.e1'], 'contains': ['112.a1', '168.b1'], 'core': '56.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [564, 2447, 8172, 7464], 'generators': [348, 224, 8], 'label': '672.1219.56.c1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '56.c1', 'normal_contained_in': ['8.c1', '28.b1', '28.e1'], 'normal_contains': ['112.a1', '168.b1'], 'normalizer': '1.a1', 'old_label': '56.c1', 'projective_image': '168.55', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439090
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '56.d1', 'aut_quo_index': 7, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': ['12.f1'], 'conjugacy_class_count': 4, 'contained_in': ['8.d1', '28.c1', '28.e1'], 'contains': ['112.a1', '168.e1'], 'core': '56.d1', 'coset_action_label': None, 'count': 4, 'diagramx': [896, 4184, 7254, 6498], 'generators': [6, 8, 224], 'label': '672.1219.56.d1', 'mobius_quo': 0, 'mobius_sub': 8, 'normal_closure': '56.d1', 'normal_contained_in': ['8.d1', '28.c1', '28.e1'], 'normal_contains': ['112.a1'], 'normalizer': '1.a1', 'old_label': '56.d1', 'projective_image': '336.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.4', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439091
{'ambient': '672.1219', 'aut_centralizer_order': 192, 'aut_label': '56.e1', 'aut_quo_index': 1, 'aut_stab_index': 24, 'aut_weyl_group': '12.4', 'aut_weyl_index': 4608, 'centralizer': '6.a1', 'complements': ['12.a1', '12.e1', '12.d1'], 'conjugacy_class_count': 24, 'contained_in': ['8.e1', '28.a1', '28.f1'], 'contains': ['112.b1', '112.c1', '168.f1'], 'core': '56.e1', 'coset_action_label': None, 'count': 24, 'diagramx': [7018, 9565, 2919, 1370], 'generators': [2, 336, 224], 'label': '672.1219.56.e1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '56.e1', 'normal_contained_in': ['8.e1', '28.a1', '28.f1'], 'normal_contains': ['112.b1', '112.c1'], 'normalizer': '1.a1', 'old_label': '56.e1', 'projective_image': '336.185', 'quotient_action_image': '1.1', 'quotient_action_kernel': '56.8', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '56.e1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439092
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '56.f1', 'aut_quo_index': 2, 'aut_stab_index': 4, 'aut_weyl_group': '12.4', 'aut_weyl_index': 4608, 'centralizer': '2.c1', 'complements': ['12.e1'], 'conjugacy_class_count': 4, 'contained_in': ['8.f1', '28.d1', '28.f1'], 'contains': ['112.b1', '168.c1'], 'core': '56.f1', 'coset_action_label': None, 'count': 4, 'diagramx': [9870, 9019, 1878, 2401], 'generators': [1, 336, 224], 'label': '672.1219.56.f1', 'mobius_quo': -2, 'mobius_sub': 0, 'normal_closure': '56.f1', 'normal_contained_in': ['8.f1', '28.d1', '28.f1'], 'normal_contains': ['112.b1', '168.c1'], 'normalizer': '1.a1', 'old_label': '56.f1', 'projective_image': '168.30', 'quotient_action_image': '2.1', 'quotient_action_kernel': '28.2', 'quotient_action_kernel_order': 28, 'quotient_fusion': None, 'short_label': '56.f1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439093
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '84.a1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 6912, 'centralizer': '1.a1', 'complements': ['8.e1'], 'conjugacy_class_count': 6, 'contained_in': ['12.a1', '28.b1', '42.a1', '42.b1'], 'contains': ['168.a1', '168.b1'], 'core': '84.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2857, 1517, 6663, 7945], 'generators': [1, 340], 'label': '672.1219.84.a1', 'mobius_quo': 0, 'mobius_sub': 6, 'normal_closure': '84.a1', 'normal_contained_in': ['12.a1', '28.b1', '42.a1'], 'normal_contains': ['168.a1', '168.b1'], 'normalizer': '1.a1', 'old_label': '84.a1', 'projective_image': '84.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '84.13', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '84.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439094
{'ambient': '672.1219', 'aut_centralizer_order': 2304, 'aut_label': '84.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '24.12', 'aut_weyl_index': 2304, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['12.b1', '28.d1', '42.a1', '42.c1', '42.d1'], 'contains': ['168.a1', '168.c1'], 'core': '84.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [8311, 3775, 3542, 5222], 'generators': [1, 8, 336], 'label': '672.1219.84.b1', 'mobius_quo': -8, 'mobius_sub': 6, 'normal_closure': '84.b1', 'normal_contained_in': ['12.b1', '28.d1', '42.a1'], 'normal_contains': ['168.a1', '168.c1'], 'normalizer': '1.a1', 'old_label': '84.b1', 'projective_image': '84.13', 'quotient_action_image': '1.1', 'quotient_action_kernel': '84.13', 'quotient_action_kernel_order': 84, 'quotient_fusion': None, 'short_label': '84.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439095
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '84.c1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 6912, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.c1', '28.a1', '42.b1', '42.c1'], 'contains': ['168.a1', '168.d1', '168.f1'], 'core': '168.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [5954, -1, 3782, -1], 'generators': [2, 8, 336], 'label': '672.1219.84.c1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '28.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.c1', 'projective_image': '168.55', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439096
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '84.d1', 'aut_quo_index': None, 'aut_stab_index': 18, 'aut_weyl_group': '8.3', 'aut_weyl_index': 6912, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 6, 'contained_in': ['12.d1', '28.c1', '42.b1', '42.d1'], 'contains': ['168.a1', '168.e1'], 'core': '168.a1', 'coset_action_label': None, 'count': 18, 'diagramx': [3494, -1, 6265, -1], 'generators': [6, 336], 'label': '672.1219.84.d1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '28.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.d1', 'projective_image': '168.55', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439097
{'ambient': '672.1219', 'aut_centralizer_order': 288, 'aut_label': '84.e1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 13824, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 16, 'contained_in': ['12.e1', '28.e1', '42.b1'], 'contains': ['168.b1', '168.d1', '168.e1'], 'core': '168.b1', 'coset_action_label': None, 'count': 48, 'diagramx': [500, -1, 7587, -1], 'generators': [2, 340], 'label': '672.1219.84.e1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '28.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.e1', 'projective_image': '168.55', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439098
{'ambient': '672.1219', 'aut_centralizer_order': 96, 'aut_label': '84.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '24.12', 'aut_weyl_index': 2304, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['12.f1', '28.f1', '42.c1'], 'contains': ['168.c1', '168.f1'], 'core': '168.c1', 'coset_action_label': None, 'count': 24, 'diagramx': [9330, -1, 1559, -1], 'generators': [1, 2, 336], 'label': '672.1219.84.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '28.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '84.f1', 'projective_image': '168.30', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '84.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439099
{'ambient': '672.1219', 'aut_centralizer_order': 32, 'aut_label': '4.a1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '288.992', 'aut_weyl_index': 192, 'centralizer': '6.a1', 'complements': [], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.b1'], 'contains': ['8.a1', '8.b1', '8.e1', '12.c1', '28.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5228, 7291, 3548, 2830], 'generators': [2, 336, 96, 8, 224], 'label': '672.1219.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1'], 'normal_contains': ['8.a1', '8.b1', '8.e1', '28.a1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '24.14', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439100
{'ambient': '672.1219', 'aut_centralizer_order': 9216, 'aut_label': '96.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '6.2', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': ['7.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '48.a1', '48.b1', '48.c1'], 'contains': ['672.a1'], 'core': '96.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5091, 4829, 3258, 3874], 'generators': [96], 'label': '672.1219.96.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '96.a1', 'normal_contained_in': ['32.a1', '48.a1', '48.b1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '96.a1', 'projective_image': '96.206', 'quotient_action_image': '1.1', 'quotient_action_kernel': '96.206', 'quotient_action_kernel_order': 96, 'quotient_fusion': None, 'short_label': '96.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439101
{'ambient': '672.1219', 'aut_centralizer_order': 27648, 'aut_label': '112.a1', 'aut_quo_index': 210, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '2.c1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['16.a1', '56.a1', '56.b1', '56.c1', '56.d1'], 'contains': ['224.a1', '336.a1'], 'core': '112.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1359, 6095, 5502, 4857], 'generators': [8, 224], 'label': '672.1219.112.a1', 'mobius_quo': 1, 'mobius_sub': -64, 'normal_closure': '112.a1', 'normal_contained_in': ['16.a1', '56.a1', '56.b1', '56.c1', '56.d1'], 'normal_contains': ['224.a1', '336.a1'], 'normalizer': '1.a1', 'old_label': '112.a1', 'projective_image': '336.226', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.13', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439102
{'ambient': '672.1219', 'aut_centralizer_order': 4608, 'aut_label': '112.b1', 'aut_quo_index': 6, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '2.c1', 'complements': ['6.b1'], 'conjugacy_class_count': 6, 'contained_in': ['16.b1', '56.a1', '56.e1', '56.f1'], 'contains': ['224.a1', '336.b1'], 'core': '112.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7152, 8777, 2989, 2800], 'generators': [336, 224], 'label': '672.1219.112.b1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '112.b1', 'normal_contained_in': ['16.b1', '56.a1', '56.e1', '56.f1'], 'normal_contains': ['224.a1', '336.b1'], 'normalizer': '1.a1', 'old_label': '112.b1', 'projective_image': '336.185', 'quotient_action_image': '2.1', 'quotient_action_kernel': '56.8', 'quotient_action_kernel_order': 56, 'quotient_fusion': None, 'short_label': '112.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439103
{'ambient': '672.1219', 'aut_centralizer_order': 1152, 'aut_label': '112.c1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': '6.1', 'aut_weyl_index': 9216, 'centralizer': '6.a1', 'complements': ['6.a1', '6.b1', '6.d1'], 'conjugacy_class_count': 8, 'contained_in': ['16.c1', '56.b1', '56.e1'], 'contains': ['224.a1', '336.c1'], 'core': '112.c1', 'coset_action_label': None, 'count': 8, 'diagramx': [4261, 9465, 3715, 2113], 'generators': [2, 224], 'label': '672.1219.112.c1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '112.c1', 'normal_contained_in': ['16.c1', '56.b1', '56.e1'], 'normal_contains': ['224.a1'], 'normalizer': '1.a1', 'old_label': '112.c1', 'projective_image': '672.1219', 'quotient_action_image': '1.1', 'quotient_action_kernel': '112.37', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '112.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 110439104
{'ambient': '672.1219', 'aut_centralizer_order': 9216, 'aut_label': '168.a1', 'aut_quo_index': 6, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['24.a1', '56.a1', '84.a1', '84.b1', '84.c1', '84.d1'], 'contains': ['336.a1', '336.b1'], 'core': '168.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5232, 3775, 4361, 5205], 'generators': [8, 336], 'label': '672.1219.168.a1', 'mobius_quo': 2, 'mobius_sub': -24, 'normal_closure': '168.a1', 'normal_contained_in': ['24.a1', '56.a1', '84.a1', '84.b1'], 'normal_contains': ['336.a1', '336.b1'], 'normalizer': '1.a1', 'old_label': '168.a1', 'projective_image': '168.55', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.55', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439105
{'ambient': '672.1219', 'aut_centralizer_order': 6912, 'aut_label': '168.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '1.a1', 'complements': ['4.f1'], 'conjugacy_class_count': 4, 'contained_in': ['24.b1', '56.c1', '84.a1', '84.e1'], 'contains': ['336.a1'], 'core': '168.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [259, 2168, 7587, 7705], 'generators': [340], 'label': '672.1219.168.b1', 'mobius_quo': 0, 'mobius_sub': -24, 'normal_closure': '168.b1', 'normal_contained_in': ['24.b1', '56.c1', '84.a1'], 'normal_contains': ['336.a1'], 'normalizer': '1.a1', 'old_label': '168.b1', 'projective_image': '168.55', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.55', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439106
{'ambient': '672.1219', 'aut_centralizer_order': 2304, 'aut_label': '168.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '6.1', 'aut_weyl_index': 9216, 'centralizer': '1.a1', 'complements': ['4.e1'], 'conjugacy_class_count': 4, 'contained_in': ['24.c1', '56.f1', '84.b1', '84.f1'], 'contains': ['336.b1'], 'core': '168.c1', 'coset_action_label': None, 'count': 4, 'diagramx': [9107, 5475, 1878, 3509], 'generators': [1, 336], 'label': '672.1219.168.c1', 'mobius_quo': 2, 'mobius_sub': 0, 'normal_closure': '168.c1', 'normal_contained_in': ['24.c1', '56.f1', '84.b1'], 'normal_contains': ['336.b1'], 'normalizer': '1.a1', 'old_label': '168.c1', 'projective_image': '168.30', 'quotient_action_image': '1.1', 'quotient_action_kernel': '168.30', 'quotient_action_kernel_order': 168, 'quotient_fusion': None, 'short_label': '168.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439107
{'ambient': '672.1219', 'aut_centralizer_order': 2304, 'aut_label': '168.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.d1', '56.b1', '84.c1', '84.e1'], 'contains': ['336.a1', '336.c1'], 'core': '336.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2216, -1, 5019, -1], 'generators': [2, 8], 'label': '672.1219.168.d1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '56.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '168.d1', 'projective_image': '336.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.d1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439108
{'ambient': '672.1219', 'aut_centralizer_order': 2304, 'aut_label': '168.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 4, 'contained_in': ['24.e1', '56.d1', '84.d1', '84.e1'], 'contains': ['336.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [823, -1, 6990, -1], 'generators': [6], 'label': '672.1219.168.e1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '56.d1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '168.e1', 'projective_image': '336.226', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.e1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439109
{'ambient': '672.1219', 'aut_centralizer_order': 384, 'aut_label': '168.f1', 'aut_quo_index': None, 'aut_stab_index': 72, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 24, 'contained_in': ['24.f1', '56.e1', '84.c1', '84.f1'], 'contains': ['336.b1', '336.c1'], 'core': '336.b1', 'coset_action_label': None, 'count': 72, 'diagramx': [6936, -1, 2764, -1], 'generators': [2, 336], 'label': '672.1219.168.f1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '56.e1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '168.f1', 'projective_image': '336.185', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '168.f1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439110
{'ambient': '672.1219', 'aut_centralizer_order': 96, 'aut_label': '4.b1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '96.221', 'aut_weyl_index': 576, 'centralizer': '2.c1', 'complements': ['168.f1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.c1'], 'contains': ['8.a1', '8.c1', '12.a1', '28.b1'], 'core': '4.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1908, 2147, 8482, 8512], 'generators': [1, 224, 96, 340, 8], 'label': '672.1219.4.b1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.b1', 'normal_contained_in': ['2.a1', '2.c1'], 'normal_contains': ['8.a1', '8.c1', '12.a1', '28.b1'], 'normalizer': '1.a1', 'old_label': '4.b1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439111
{'ambient': '672.1219', 'aut_centralizer_order': 27648, 'aut_label': '224.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 27648, 'centralizer': '2.c1', 'complements': ['3.a1'], 'conjugacy_class_count': 1, 'contained_in': ['32.a1', '112.a1', '112.b1', '112.c1'], 'contains': ['672.a1'], 'core': '224.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4261, 8809, 3679, 3144], 'generators': [224], 'label': '672.1219.224.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '224.a1', 'normal_contained_in': ['32.a1', '112.a1', '112.b1', '112.c1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '224.a1', 'projective_image': '672.1219', 'quotient_action_image': '2.1', 'quotient_action_kernel': '112.37', 'quotient_action_kernel_order': 112, 'quotient_fusion': None, 'short_label': '224.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 110439112
{'ambient': '672.1219', 'aut_centralizer_order': 55296, 'aut_label': '336.a1', 'aut_quo_index': 14, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 55296, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['48.a1', '112.a1', '168.a1', '168.b1', '168.d1', '168.e1'], 'contains': ['672.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1705, 3775, 5268, 5205], 'generators': [8], 'label': '672.1219.336.a1', 'mobius_quo': -1, 'mobius_sub': 192, 'normal_closure': '336.a1', 'normal_contained_in': ['48.a1', '112.a1', '168.a1', '168.b1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '336.a1', 'projective_image': '336.226', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.226', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439113
{'ambient': '672.1219', 'aut_centralizer_order': 9216, 'aut_label': '336.b1', 'aut_quo_index': 1, 'aut_stab_index': 6, 'aut_weyl_group': '1.1', 'aut_weyl_index': 55296, 'centralizer': '1.a1', 'complements': ['2.a1'], 'conjugacy_class_count': 6, 'contained_in': ['48.b1', '112.b1', '168.a1', '168.c1', '168.f1'], 'contains': ['672.a1'], 'core': '336.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [7081, 5119, 2878, 3565], 'generators': [336], 'label': '672.1219.336.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.b1', 'normal_contained_in': ['48.b1', '112.b1', '168.a1', '168.c1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '336.b1', 'projective_image': '336.185', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.185', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439114
{'ambient': '672.1219', 'aut_centralizer_order': 2304, 'aut_label': '336.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 55296, 'centralizer': '3.a1', 'complements': None, 'conjugacy_class_count': 8, 'contained_in': ['48.c1', '112.c1', '168.d1', '168.f1'], 'contains': ['672.a1'], 'core': '672.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5202, -1, 3469, -1], 'generators': [2], 'label': '672.1219.336.c1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '112.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1', 'old_label': '336.c1', 'projective_image': '672.1219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '336.c1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439115
{'ambient': '672.1219', 'aut_centralizer_order': None, 'aut_label': '672.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': ['1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['96.a1', '224.a1', '336.a1', '336.b1', '336.c1'], 'contains': [], 'core': '672.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5202, 4976, 3469, 3719], 'generators': [], 'label': '672.1219.672.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '672.a1', 'normal_contained_in': ['96.a1', '224.a1', '336.a1', '336.b1'], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '672.a1', 'projective_image': '672.1219', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '672.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 110439116
{'ambient': '672.1219', 'aut_centralizer_order': 32, 'aut_label': '4.c1', 'aut_quo_index': 3, 'aut_stab_index': 6, 'aut_weyl_group': '288.992', 'aut_weyl_index': 192, 'centralizer': '6.a1', 'complements': ['168.f1'], 'conjugacy_class_count': 6, 'contained_in': ['2.a1', '2.d1'], 'contains': ['8.a1', '8.d1', '12.d1', '28.c1'], 'core': '4.c1', 'coset_action_label': None, 'count': 6, 'diagramx': [3675, 4992, 6806, 5355], 'generators': [6, 96, 8, 336, 224], 'label': '672.1219.4.c1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.c1', 'normal_contained_in': ['2.a1', '2.d1'], 'normal_contains': ['8.a1', '8.d1', '28.c1'], 'normalizer': '1.a1', 'old_label': '4.c1', 'projective_image': '24.14', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.c1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
