-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 4, 4, 4, 6], 'aut_gens': [[1, 4, 12, 24, 48, 192], [483, 388, 12, 24, 48, 192], [1, 704, 492, 420, 192, 48], [337, 340, 348, 312, 48, 192], [253, 364, 396, 24, 48, 288], [707, 232, 504, 132, 240, 144]], 'aut_group': '6144.ze', 'aut_hash': 4158378184127417885, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 48, 'aut_perms': [786994716121995845792088968048593973692851389545583914003779, 1246985194082895749080075359288105737375666239914157369, 6099352358899537785535488743667560434063723627157271849941760, 5825331355524962715358235260341732302867931016034451050107460, 10522959519918743711937774685771173828696886487635544566897714], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 2, 2], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 2], [4, 24, 2, 2], [4, 48, 4, 1], [6, 128, 1, 1], [8, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^3:(C_2^2\\times S_4)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '3072.bgb', 'autcentquo_hash': 7983714371117797868, 'autcentquo_nilpotent': False, 'autcentquo_order': 3072, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^3:(C_2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 4], [3, 128, 1], [4, 12, 2], [4, 24, 6], [4, 48, 4], [6, 128, 1], [8, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '384.18135', 'commutator_count': 1, 'commutator_label': '192.1023', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1088652, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 4], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 2], [4, 24, 2, 2], [4, 48, 2, 2], [6, 128, 1, 1], [8, 48, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 18, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 0, 2]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '96.227', 'hash': 1088652, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 3, 2, 2, 4, 4], 'inner_gens': [[1, 8, 12, 36, 672, 528], [9, 4, 24, 36, 240, 432], [1, 40, 12, 24, 432, 288], [13, 16, 12, 24, 528, 576], [337, 580, 396, 504, 48, 192], [625, 724, 108, 408, 48, 192]], 'inner_hash': 18135, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': True, 'inner_tex': 'C_4^2:S_4', 'inner_used': [1, 2, 3, 5], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 2], [12, 4]], 'label': '768.1088652', 'linC_count': 2, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 14, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^5.S4', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 24, 'number_divisions': 19, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 198, 'number_subgroup_classes': 308, 'number_subgroups': 3140, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 55], [3, 128], [4, 360], [6, 128], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 240, 0, 480], 'outer_gens': [[1, 40, 12, 24, 528, 672], [1, 88, 252, 696, 528, 672], [3, 4, 12, 24, 48, 192], [1, 436, 12, 504, 48, 192]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 415, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [3, 6], [6, 5], [12, 2], [24, 1]], 'representations': {'PC': {'code': '78327259499916589785263670325175977639395778892494820927444427817536', 'gens': [1, 3, 4, 5, 6, 8], 'pres': [9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 18, 218, 237, 1624, 427, 36293, 3263, 1976, 1229, 158, 24198, 7584, 38023, 7801, 1762, 1771, 214, 7784, 1970]}, 'Perm': {'d': 20, 'gens': [26156162887103649, 16, 7521776674635720, 34546840397763240, 41305012191118800, 122780164178650440, 269076285630005040, 400159604658926880, 534431552601219960]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5.S_4', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
-
gps_conj_classes • Show schema
Hide schema
-
id: 110943220
{'aut_label': '1A', 'centralizer': '1.a1.a1', 'counter': 1, 'group_counter': 1088652, 'group_order': 768, 'label': '1A', 'order': 1, 'powers': [1, 1], 'representative': 0, 'size': 1}
-
id: 110943231
{'aut_label': '2A', 'centralizer': '1.a1.a1', 'counter': 2, 'group_counter': 1088652, 'group_order': 768, 'label': '2A', 'order': 2, 'powers': [1, 2], 'representative': 2, 'size': 1}
-
id: 110943237
{'aut_label': '2B', 'centralizer': '3.a1.a1', 'counter': 3, 'group_counter': 1088652, 'group_order': 768, 'label': '2B', 'order': 2, 'powers': [1, 3], 'representative': 384, 'size': 3}
-
id: 110943238
{'aut_label': '2C', 'centralizer': '3.a1.a1', 'counter': 4, 'group_counter': 1088652, 'group_order': 768, 'label': '2C', 'order': 2, 'powers': [1, 4], 'representative': 482, 'size': 3}
-
id: 110943239
{'aut_label': '2D', 'centralizer': '12.h1.a1', 'counter': 5, 'group_counter': 1088652, 'group_order': 768, 'label': '2D', 'order': 2, 'powers': [1, 5], 'representative': 24, 'size': 12}
-
id: 110943240
{'aut_label': '2D', 'centralizer': '12.h1.b1', 'counter': 6, 'group_counter': 1088652, 'group_order': 768, 'label': '2E', 'order': 2, 'powers': [1, 6], 'representative': 216, 'size': 12}
-
id: 110943241
{'aut_label': '2F', 'centralizer': '12.h1.b1', 'counter': 7, 'group_counter': 1088652, 'group_order': 768, 'label': '2F', 'order': 2, 'powers': [1, 7], 'representative': 602, 'size': 12}
-
id: 110943242
{'aut_label': '2F', 'centralizer': '12.h1.a1', 'counter': 8, 'group_counter': 1088652, 'group_order': 768, 'label': '2G', 'order': 2, 'powers': [1, 8], 'representative': 506, 'size': 12}
-
id: 110943243
{'aut_label': '3A', 'centralizer': '128.a1.a1', 'counter': 9, 'group_counter': 1088652, 'group_order': 768, 'label': '3A', 'order': 3, 'powers': [9, 1], 'representative': 688, 'size': 128}
-
id: 110943221
{'aut_label': '4A', 'centralizer': '12.k1.a1', 'counter': 10, 'group_counter': 1088652, 'group_order': 768, 'label': '4A', 'order': 4, 'powers': [3, 10], 'representative': 192, 'size': 12}
-
id: 110943222
{'aut_label': '4B', 'centralizer': '12.k1.a1', 'counter': 11, 'group_counter': 1088652, 'group_order': 768, 'label': '4B', 'order': 4, 'powers': [3, 11], 'representative': 626, 'size': 12}
-
id: 110943223
{'aut_label': '4C', 'centralizer': '24.r1.a1', 'counter': 12, 'group_counter': 1088652, 'group_order': 768, 'label': '4C', 'order': 4, 'powers': [3, 12], 'representative': 72, 'size': 24}
-
id: 110943224
{'aut_label': '4D', 'centralizer': '24.r1.a1', 'counter': 13, 'group_counter': 1088652, 'group_order': 768, 'label': '4D', 'order': 4, 'powers': [3, 13], 'representative': 74, 'size': 24}
-
id: 110943225
{'aut_label': '4E1', 'centralizer': '24.d1.a1', 'counter': 14, 'group_counter': 1088652, 'group_order': 768, 'label': '4E1', 'order': 4, 'powers': [2, 15], 'representative': 1, 'size': 24}
-
id: 110943226
{'aut_label': '4E1', 'centralizer': '24.d1.a1', 'counter': 15, 'group_counter': 1088652, 'group_order': 768, 'label': '4E-1', 'order': 4, 'powers': [2, 14], 'representative': 3, 'size': 24}
-
id: 110943227
{'aut_label': '4F1', 'centralizer': '24.c1.a1', 'counter': 16, 'group_counter': 1088652, 'group_order': 768, 'label': '4F1', 'order': 4, 'powers': [4, 17], 'representative': 385, 'size': 24}
-
id: 110943228
{'aut_label': '4F1', 'centralizer': '24.c1.a1', 'counter': 17, 'group_counter': 1088652, 'group_order': 768, 'label': '4F-1', 'order': 4, 'powers': [4, 16], 'representative': 387, 'size': 24}
-
id: 110943229
{'aut_label': '4G1', 'centralizer': '48.f1.b1', 'counter': 18, 'group_counter': 1088652, 'group_order': 768, 'label': '4G1', 'order': 4, 'powers': [7, 19], 'representative': 383, 'size': 48}
-
id: 110943230
{'aut_label': '4G1', 'centralizer': '48.f1.b1', 'counter': 19, 'group_counter': 1088652, 'group_order': 768, 'label': '4G-1', 'order': 4, 'powers': [7, 18], 'representative': 69, 'size': 48}
-
id: 110943232
{'aut_label': '4G1', 'centralizer': '48.f1.a1', 'counter': 20, 'group_counter': 1088652, 'group_order': 768, 'label': '4H1', 'order': 4, 'powers': [8, 21], 'representative': 311, 'size': 48}
-
id: 110943233
{'aut_label': '4G1', 'centralizer': '48.f1.a1', 'counter': 21, 'group_counter': 1088652, 'group_order': 768, 'label': '4H-1', 'order': 4, 'powers': [8, 20], 'representative': 237, 'size': 48}
-
id: 110943234
{'aut_label': '6A', 'centralizer': '128.a1.a1', 'counter': 22, 'group_counter': 1088652, 'group_order': 768, 'label': '6A', 'order': 6, 'powers': [9, 2], 'representative': 382, 'size': 128}
-
id: 110943235
{'aut_label': '8A1', 'centralizer': '48.n1.a1', 'counter': 23, 'group_counter': 1088652, 'group_order': 768, 'label': '8A1', 'order': 8, 'powers': [11, 24], 'representative': 63, 'size': 48}
-
id: 110943236
{'aut_label': '8A1', 'centralizer': '48.n1.a1', 'counter': 24, 'group_counter': 1088652, 'group_order': 768, 'label': '8A-1', 'order': 8, 'powers': [11, 23], 'representative': 205, 'size': 48}
-
gps_qchar • Show schema
Hide schema
-
id: 4799172
{'cdim': 1, 'counter': 1, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.1a', 'multiplicity': 1, 'nt': [1, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'schur_index': 1}
-
id: 4799183
{'cdim': 1, 'counter': 2, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.1b', 'multiplicity': 1, 'nt': [2, 1], 'qdim': 1, 'qvalues': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, -1], 'schur_index': 1}
-
id: 4799184
{'cdim': 1, 'counter': 3, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.1c', 'multiplicity': 2, 'nt': [4, 1], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, 2, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0], 'schur_index': 1}
-
id: 4799185
{'cdim': 2, 'counter': 4, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.2a', 'multiplicity': 1, 'nt': [3, 2], 'qdim': 2, 'qvalues': [2, 2, 2, 2, 2, 2, 2, 2, -1, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0], 'schur_index': 1}
-
id: 4799186
{'cdim': 2, 'counter': 5, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.2b', 'multiplicity': 1, 'nt': [12, 5], 'qdim': 2, 'qvalues': [2, -2, 2, -2, -2, 2, 2, -2, -1, 2, -2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0], 'schur_index': 2}
-
id: 4799187
{'cdim': 3, 'counter': 6, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3a', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 0, 3, 3, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 0, 1, 1], 'schur_index': 1}
-
id: 4799188
{'cdim': 3, 'counter': 7, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3b', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, 3, -1, 3, 0, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 0, -1, -1], 'schur_index': 1}
-
id: 4799189
{'cdim': 3, 'counter': 8, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3c', 'multiplicity': 1, 'nt': [4, 5], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, -1, 3, -1, 0, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, 1, 0, -1, -1], 'schur_index': 1}
-
id: 4799190
{'cdim': 3, 'counter': 9, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3d', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, -1, -1, -1, 0, 3, 3, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 0, -1, -1], 'schur_index': 1}
-
id: 4799173
{'cdim': 3, 'counter': 10, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3e', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, -1, 3, -1, 3, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 0, 1, 1], 'schur_index': 1}
-
id: 4799174
{'cdim': 3, 'counter': 11, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3f', 'multiplicity': 1, 'nt': [6, 8], 'qdim': 3, 'qvalues': [3, 3, 3, 3, 3, -1, 3, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 0, 1, 1], 'schur_index': 1}
-
id: 4799175
{'cdim': 3, 'counter': 12, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3g', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, -6, 6, -6, -6, -2, 6, 2, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799176
{'cdim': 3, 'counter': 13, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3h', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 2, -2, -2, 2, 0, 6, -6, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799177
{'cdim': 3, 'counter': 14, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.3i', 'multiplicity': 2, 'nt': [12, 27], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 2, 6, -2, -6, 0, -2, 2, -2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799178
{'cdim': 6, 'counter': 15, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.6a', 'multiplicity': 1, 'nt': [8, 34], 'qdim': 6, 'qvalues': [6, 6, 6, 6, -2, -2, -2, -2, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799179
{'cdim': 6, 'counter': 16, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.6b', 'multiplicity': 1, 'nt': [12, 102], 'qdim': 6, 'qvalues': [6, -6, 6, -6, 2, -2, -2, 2, 0, -2, 2, 2, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799180
{'cdim': 12, 'counter': 17, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.12a', 'multiplicity': 1, 'nt': [16, 776], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -2, -2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799181
{'cdim': 12, 'counter': 18, 'faithful': False, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.12b', 'multiplicity': 1, 'nt': [24, 985], 'qdim': 12, 'qvalues': [12, 12, -4, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, -2, 2, 2, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
id: 4799182
{'cdim': 12, 'counter': 19, 'faithful': True, 'group': '768.1088652', 'group_order': 768, 'image': None, 'label': '768.1088652.12c', 'multiplicity': 2, 'nt': [48, 0], 'qdim': 24, 'qvalues': [24, -24, -8, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'schur_index': 1}
-
gps_char • Show schema
Hide schema
-
id: 7845058
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 768, 'counter': 1, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '1.1', 'image_order': 1, 'indicator': 1, 'kernel': '1.a1.a1', 'kernel_order': 768, 'label': '768.1088652.1a', 'nt': [1, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]]]}
-
id: 7845069
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 768, 'counter': 2, 'cyclotomic_n': 1, 'dim': 1, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '2.1', 'image_order': 2, 'indicator': 1, 'kernel': '2.a1.a1', 'kernel_order': 384, 'label': '768.1088652.1b', 'nt': [2, 1], 'q_character': None, 'values': [[[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 7845075
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 768, 'counter': 3, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 192, 'label': '768.1088652.1c1', 'nt': [4, 1], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 0]], [[1, 1]], [[-1, 1]]]}
-
id: 7845076
{'center': '1.a1.a1', 'center_index': 1, 'center_order': 768, 'counter': 4, 'cyclotomic_n': 4, 'dim': 1, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '4.1', 'image_order': 4, 'indicator': 0, 'kernel': '4.a1.a1', 'kernel_order': 192, 'label': '768.1088652.1c2', 'nt': [4, 2], 'q_character': None, 'values': [[[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 0]], [[-1, 1]], [[1, 1]]]}
-
id: 7845077
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 128, 'counter': 5, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '6.1', 'image_order': 6, 'indicator': 1, 'kernel': '6.a1.a1', 'kernel_order': 128, 'label': '768.1088652.2a', 'nt': [3, 2], 'q_character': None, 'values': [[[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[-1, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-1, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845078
{'center': '6.a1.a1', 'center_index': 6, 'center_order': 128, 'counter': 6, 'cyclotomic_n': 1, 'dim': 2, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '12.1', 'image_order': 12, 'indicator': -1, 'kernel': '12.a1.a1', 'kernel_order': 64, 'label': '768.1088652.2b', 'nt': [12, 5], 'q_character': None, 'values': [[[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-1, 0]], [[2, 0]], [[-2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[1, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845079
{'center': '24.b1.a1', 'center_index': 24, 'center_order': 32, 'counter': 7, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 32, 'label': '768.1088652.3a', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
-
id: 7845080
{'center': '24.a1.b1', 'center_index': 24, 'center_order': 32, 'counter': 8, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.b1', 'kernel_order': 32, 'label': '768.1088652.3b', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 7845081
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 32, 'counter': 9, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 32, 'label': '768.1088652.3c', 'nt': [4, 5], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 7845059
{'center': '24.b1.a1', 'center_index': 24, 'center_order': 32, 'counter': 10, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.b1.a1', 'kernel_order': 32, 'label': '768.1088652.3d', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]]]}
-
id: 7845060
{'center': '24.a1.b1', 'center_index': 24, 'center_order': 32, 'counter': 11, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.b1', 'kernel_order': 32, 'label': '768.1088652.3e', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
-
id: 7845061
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 32, 'counter': 12, 'cyclotomic_n': 1, 'dim': 3, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '24.12', 'image_order': 24, 'indicator': 1, 'kernel': '24.a1.a1', 'kernel_order': 32, 'label': '768.1088652.3f', 'nt': [6, 8], 'q_character': None, 'values': [[[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[3, 0]], [[-1, 0]], [[3, 0]], [[-1, 0]], [[0, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[0, 0]], [[1, 0]], [[1, 0]]]}
-
id: 7845062
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 32, 'counter': 13, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 16, 'label': '768.1088652.3g1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]]]}
-
id: 7845063
{'center': '24.a1.a1', 'center_index': 24, 'center_order': 32, 'counter': 14, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.a1', 'kernel_order': 16, 'label': '768.1088652.3g2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[-3, 0]], [[-1, 0]], [[3, 0]], [[1, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]]]}
-
id: 7845064
{'center': '24.b1.a1', 'center_index': 24, 'center_order': 32, 'counter': 15, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 16, 'label': '768.1088652.3h1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]]]}
-
id: 7845065
{'center': '24.b1.a1', 'center_index': 24, 'center_order': 32, 'counter': 16, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.b1.a1', 'kernel_order': 16, 'label': '768.1088652.3h2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[-1, 0]], [[-1, 0]], [[1, 0]], [[0, 0]], [[3, 0]], [[-3, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]]]}
-
id: 7845066
{'center': '24.a1.b1', 'center_index': 24, 'center_order': 32, 'counter': 17, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.b1', 'kernel_order': 16, 'label': '768.1088652.3i1', 'nt': [12, 27], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[0, 0]], [[-1, 1]], [[1, 1]]]}
-
id: 7845067
{'center': '24.a1.b1', 'center_index': 24, 'center_order': 32, 'counter': 18, 'cyclotomic_n': 4, 'dim': 3, 'faithful': False, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '48.30', 'image_order': 48, 'indicator': 0, 'kernel': '48.a1.b1', 'kernel_order': 16, 'label': '768.1088652.3i2', 'nt': [12, 2], 'q_character': None, 'values': [[[3, 0]], [[-3, 0]], [[3, 0]], [[-3, 0]], [[1, 0]], [[3, 0]], [[-1, 0]], [[-3, 0]], [[0, 0]], [[-1, 0]], [[1, 0]], [[-1, 0]], [[1, 0]], [[1, 1]], [[-1, 1]], [[1, 1]], [[-1, 1]], [[-1, 1]], [[1, 1]], [[1, 1]], [[-1, 1]], [[0, 0]], [[1, 1]], [[-1, 1]]]}
-
id: 7845068
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 8, 'counter': 19, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '96.227', 'image_order': 96, 'indicator': 1, 'kernel': '96.a1.a1', 'kernel_order': 8, 'label': '768.1088652.6a', 'nt': [8, 34], 'q_character': None, 'values': [[[6, 0]], [[6, 0]], [[6, 0]], [[6, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845070
{'center': '96.a1.a1', 'center_index': 96, 'center_order': 8, 'counter': 20, 'cyclotomic_n': 1, 'dim': 6, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '192.1495', 'image_order': 192, 'indicator': 1, 'kernel': '192.a1.a1', 'kernel_order': 4, 'label': '768.1088652.6b', 'nt': [12, 102], 'q_character': None, 'values': [[[6, 0]], [[-6, 0]], [[6, 0]], [[-6, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[0, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845071
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 21, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '384.18135', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 2, 'label': '768.1088652.12a', 'nt': [16, 776], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 0]], [[2, 0]], [[-2, 0]], [[-2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845072
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 22, 'cyclotomic_n': 1, 'dim': 12, 'faithful': False, 'field': [0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '384.18135', 'image_order': 384, 'indicator': 1, 'kernel': '384.a1.a1', 'kernel_order': 2, 'label': '768.1088652.12b', 'nt': [24, 985], 'q_character': None, 'values': [[[12, 0]], [[12, 0]], [[-4, 0]], [[-4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 0]], [[-2, 0]], [[2, 0]], [[2, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845073
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 23, 'cyclotomic_n': 4, 'dim': 12, 'faithful': True, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '768.1088652', 'image_order': 768, 'indicator': 0, 'kernel': '768.a1.a1', 'kernel_order': 1, 'label': '768.1088652.12c1', 'nt': [48, 0], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[-2, 1]], [[2, 1]], [[2, 1]], [[-2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
id: 7845074
{'center': '384.a1.a1', 'center_index': 384, 'center_order': 2, 'counter': 24, 'cyclotomic_n': 4, 'dim': 12, 'faithful': True, 'field': [1, 0, 1], 'group': '768.1088652', 'group_counter': 1088652, 'group_order': 768, 'image': None, 'image_isoclass': '768.1088652', 'image_order': 768, 'indicator': 0, 'kernel': '768.a1.a1', 'kernel_order': 1, 'label': '768.1088652.12c2', 'nt': [48, 2], 'q_character': None, 'values': [[[12, 0]], [[-12, 0]], [[-4, 0]], [[4, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[2, 1]], [[-2, 1]], [[-2, 1]], [[2, 1]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]], [[0, 0]]]}
-
gps_subgroup_search • Show schema
Hide schema
-
id: 68514808
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 768, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '768.1088652.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '768.1088652', 'subgroup_hash': 1088652, 'subgroup_order': 768, 'subgroup_tex': 'C_2^5.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514919
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 384, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.2.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '384.18231', 'subgroup_hash': 18231, 'subgroup_order': 384, 'subgroup_tex': 'C_2^5:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515030
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 128, 'counter': 3, 'cyclic': False, 'direct': None, 'hall': 2, 'label': '768.1088652.3.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 3, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '256.5751', 'subgroup_hash': 5751, 'subgroup_order': 256, 'subgroup_tex': 'C_2^5.D_4', 'supersolvable': True, 'sylow': 2}
-
id: 68515050
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': True, 'core_order': 192, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.4.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', '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': ['D', 'L1', 'D1', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1023', 'subgroup_hash': 1023, 'subgroup_order': 192, 'subgroup_tex': 'C_4^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515061
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.4.b1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515072
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 6, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.4.b1.b1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.1495', 'subgroup_hash': 1495, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515083
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 7, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.4.c1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 4, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '192.182', 'subgroup_hash': 182, 'subgroup_order': 192, 'subgroup_tex': 'C_2^3.S_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515094
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 128, 'counter': 8, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.6.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '6.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 6, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'S_3', 'simple': False, 'solvable': True, 'special_labels': ['F'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '128.2258', 'subgroup_hash': 2258, 'subgroup_order': 128, 'subgroup_tex': 'C_4^2:C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68515105
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 9, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.617', 'subgroup_hash': 617, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514809
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 10, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.857', 'subgroup_hash': 857, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514820
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 11, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514831
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.621', 'subgroup_hash': 621, 'subgroup_order': 128, 'subgroup_tex': 'C_2^4.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514842
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 13, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514853
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.6.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '6.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 6, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '128.850', 'subgroup_hash': 850, 'subgroup_order': 128, 'subgroup_tex': 'C_2^5:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514864
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 15, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.8.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514875
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 16, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.8.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.229', 'subgroup_hash': 229, 'subgroup_order': 96, 'subgroup_tex': 'C_2^3:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514886
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 32, 'counter': 17, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.8.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 68514897
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 18, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.8.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '96.68', 'subgroup_hash': 68, 'subgroup_order': 96, 'subgroup_tex': 'C_4^2:C_6', 'supersolvable': False, 'sylow': 0}
-
id: 68514908
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 64, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.1', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3:C_4', 'simple': False, 'solvable': True, 'special_labels': ['D2', 'C3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514920
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514931
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 21, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.23', 'subgroup_hash': 23, 'subgroup_order': 64, 'subgroup_tex': 'C_2^2.C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514942
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 22, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514953
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.199', 'subgroup_hash': 199, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514964
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 24, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514975
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 25, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.90', 'subgroup_hash': 90, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514986
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 26, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514997
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 27, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.207', 'subgroup_hash': 207, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515008
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 28, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515019
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 29, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.60', 'subgroup_hash': 60, 'subgroup_order': 64, 'subgroup_tex': 'C_2^4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515031
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 30, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515041
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.202', 'subgroup_hash': 202, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3:D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515042
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 8, 'counter': 32, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.100', 'subgroup_hash': 100, 'subgroup_order': 64, 'subgroup_tex': 'C_2^3.D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515043
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 32, 'counter': 33, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.20', 'subgroup_hash': 20, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515044
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 34, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515045
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 35, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515046
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515047
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 37, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515048
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 38, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515049
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 39, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.32', 'subgroup_hash': 32, 'subgroup_order': 64, 'subgroup_tex': 'C_2\\wr C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515051
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 40, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515052
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.242', 'subgroup_hash': 242, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515053
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 42, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515054
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 16, 'counter': 43, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.12.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '12.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 12, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '64.35', 'subgroup_hash': 35, 'subgroup_order': 64, 'subgroup_tex': 'C_4^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515055
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 44, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515056
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 45, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515057
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 46, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.b1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515058
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 47, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515059
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 48, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.b1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.b1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.30', 'subgroup_hash': 30, 'subgroup_order': 48, 'subgroup_tex': 'A_4:C_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515060
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515062
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 50, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.50', 'subgroup_hash': 50, 'subgroup_order': 48, 'subgroup_tex': 'C_2^2:A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68515063
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 16, 'counter': 51, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 68515064
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.16.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '16.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 16, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '48.3', 'subgroup_hash': 3, 'subgroup_order': 48, 'subgroup_tex': 'C_4^2:C_3', 'supersolvable': False, 'sylow': 0}
-
id: 68515065
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 53, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.24.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 68515066
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 32, 'counter': 54, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.24.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
-
id: 68515067
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 55, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.24.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '24.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.12', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 12, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'S_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515068
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 56, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515069
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 57, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.25', 'subgroup_hash': 25, 'subgroup_order': 32, 'subgroup_tex': 'C_4\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515070
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 58, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515071
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515073
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 60, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515074
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 61, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515075
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 62, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515076
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 2, 'counter': 63, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.10', 'subgroup_hash': 10, 'subgroup_order': 32, 'subgroup_tex': 'Q_8:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515077
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 64, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515078
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 65, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515079
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 66, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515080
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 67, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515081
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 68, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515082
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 69, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.k1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.k1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515084
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 70, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515085
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 71, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.22', 'subgroup_hash': 22, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515086
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 72, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515087
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 73, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.46', 'subgroup_hash': 46, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515088
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 74, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.47', 'subgroup_hash': 47, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68515089
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 75, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.24', 'subgroup_hash': 24, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515090
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 8, 'counter': 76, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.37', 'subgroup_hash': 37, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times \\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68515091
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.21', 'subgroup_hash': 21, 'subgroup_order': 32, 'subgroup_tex': 'C_2\\times C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515092
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 78, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515093
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 79, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515095
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 80, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515096
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 81, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515097
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 82, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515098
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 83, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.u1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.u1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515099
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 84, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515100
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 85, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.v1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.v1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515101
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 86, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515102
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 87, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.7', 'subgroup_hash': 7, 'subgroup_order': 32, 'subgroup_tex': '\\OD_{16}:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515103
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 88, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515104
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 89, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.x1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.x1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515106
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 90, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515107
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 91, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.y1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.y1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515108
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 92, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515109
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 93, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515110
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 94, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515111
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 95, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515112
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 96, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515113
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 97, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515114
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 98, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515115
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 99, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514810
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 100, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514811
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 101, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514812
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 102, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514813
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 103, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.27', 'subgroup_hash': 27, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\wr C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514814
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 104, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514815
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 105, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514816
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 106, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514817
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 4, 'counter': 107, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.6', 'subgroup_hash': 6, 'subgroup_order': 32, 'subgroup_tex': 'C_2^3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514818
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 16, 'counter': 108, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514819
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 109, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.24.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '24.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 24, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.31', 'subgroup_hash': 31, 'subgroup_order': 32, 'subgroup_tex': 'C_4^2:C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68514821
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 8, 'counter': 110, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514822
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 111, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514823
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 112, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514824
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 113, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514825
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 114, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514826
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 115, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514827
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 116, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.32.b2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '32.b2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 32, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '24.13', 'subgroup_hash': 13, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514828
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 117, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.48.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514829
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 16, 'counter': 118, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.48.a1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.a1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514830
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 16, 'counter': 119, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.48.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '48.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '48.30', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 30, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514832
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 120, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514833
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 121, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514834
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 122, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514835
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 123, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514836
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 124, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514837
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 125, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514838
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 126, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514839
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 127, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514840
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 128, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514841
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 129, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514843
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 130, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514844
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 131, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514845
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 132, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514846
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 133, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514847
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 134, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514848
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 135, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.4', 'subgroup_hash': 4, 'subgroup_order': 16, 'subgroup_tex': 'C_4:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514849
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 136, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.5', 'subgroup_hash': 5, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times C_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514850
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 137, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514851
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 138, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514852
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 139, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514854
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 8, 'counter': 140, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.10', 'subgroup_hash': 10, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514855
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 8, 'counter': 141, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514856
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 142, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514857
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 143, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.s1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514858
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 144, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514859
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.s1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.s1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514860
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 146, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514861
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 147, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.t1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.t1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514862
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 148, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514863
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 149, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514865
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 150, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514866
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 151, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.w1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.w1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514867
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 152, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514868
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 153, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68514869
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 154, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514870
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 155, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514871
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 156, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514872
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 157, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514873
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 158, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514874
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 159, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bb1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bb1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.14', 'subgroup_hash': 14, 'subgroup_order': 16, 'subgroup_tex': 'C_2^4', 'supersolvable': True, 'sylow': 0}
-
id: 68514876
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 160, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514877
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 161, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bc1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bc1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514878
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 162, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514879
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 163, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bd1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bd1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514880
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 164, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514881
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 165, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.be1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.be1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514882
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 166, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514883
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 167, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514884
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 168, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514885
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 169, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514887
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 170, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bi1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514888
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 171, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bi1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bi1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514889
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 172, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bj1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514890
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 173, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bj1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bj1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514891
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 174, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bk1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514892
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 175, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bk1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bk1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514893
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 176, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bl1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514894
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 177, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bl1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bl1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514895
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 178, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bm1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bm1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514896
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 179, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bn1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bn1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.11', 'subgroup_hash': 11, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514898
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 180, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bo1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bo1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514899
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 181, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bp1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bp1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514900
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 182, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bq1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bq1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514901
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 183, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.br1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.br1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.12', 'subgroup_hash': 12, 'subgroup_order': 16, 'subgroup_tex': 'C_2\\times Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514902
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 4, 'counter': 184, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bs1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bs1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.6', 'subgroup_hash': 6, 'subgroup_order': 16, 'subgroup_tex': '\\OD_{16}', 'supersolvable': True, 'sylow': 0}
-
id: 68514903
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 185, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bt1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bt1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514904
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 186, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bu1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bu1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.2', 'subgroup_hash': 2, 'subgroup_order': 16, 'subgroup_tex': 'C_4^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514905
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 187, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bv1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514906
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 188, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bv1.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514907
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 189, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bv1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514909
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 190, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.48.bv1.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '48.bv1.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 48, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '16.3', 'subgroup_hash': 3, 'subgroup_order': 16, 'subgroup_tex': 'C_2^2:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514910
{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2, 'counter': 191, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.1', 'subgroup_hash': 1, 'subgroup_order': 12, 'subgroup_tex': 'C_3:C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514911
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 4, 'counter': 192, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514912
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 193, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514913
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 194, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514914
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 195, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514915
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 196, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514916
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 197, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514917
{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1, 'counter': 198, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.64.c2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '64.c2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 64, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '12.3', 'subgroup_hash': 3, 'subgroup_order': 12, 'subgroup_tex': 'A_4', 'supersolvable': False, 'sylow': 0}
-
id: 68514918
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 8, 'counter': 199, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.96.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '96.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '96.227', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 227, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 96, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^2:S_4', 'simple': False, 'solvable': True, 'special_labels': ['Phi', 'S'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514921
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 200, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514922
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 201, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.b1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514923
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 202, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.b2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514924
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 203, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.b2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.b2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514925
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 204, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514926
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 205, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514927
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 206, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514928
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 207, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514929
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 208, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514930
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 209, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514932
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 210, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514933
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 2, 'counter': 211, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.h1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.h1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514934
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 212, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514935
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 213, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514936
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 214, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514937
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 215, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514938
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 216, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514939
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 217, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.i2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.i2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514940
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 218, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514941
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 219, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.j1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514943
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 220, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.j2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514944
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 221, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.j2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.j2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514945
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 222, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514946
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 223, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514947
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 224, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514948
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 225, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.m1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.m1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514949
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 226, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514950
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 227, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514951
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 228, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514952
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 229, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514954
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 230, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.o2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514955
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 231, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.o2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.o2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514956
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 232, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514957
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 233, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.q1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.q1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514958
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 234, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.r1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514959
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 235, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.r1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.r1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514960
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 236, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.s1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514961
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 237, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.s1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.s1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514962
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 238, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.t1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.t1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514963
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 239, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.u1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.u1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.3', 'subgroup_hash': 3, 'subgroup_order': 8, 'subgroup_tex': 'D_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514965
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 240, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.v1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.v1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514966
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 241, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.w1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.w1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514967
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 1, 'counter': 242, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.x1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.x1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.4', 'subgroup_hash': 4, 'subgroup_order': 8, 'subgroup_tex': 'Q_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514968
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 243, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.96.y1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.y1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.1', 'subgroup_hash': 1, 'subgroup_order': 8, 'subgroup_tex': 'C_8', 'supersolvable': True, 'sylow': 0}
-
id: 68514969
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 244, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514970
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 245, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.z1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.z1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514971
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 246, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.ba1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514972
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 247, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.ba1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.ba1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514973
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 248, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bb1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bb1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514974
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 249, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bc1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bc1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514976
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 250, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bd1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bd1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514977
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 4, 'counter': 251, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.be1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.be1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514978
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 252, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bf1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514979
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 253, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bf1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bf1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514980
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 254, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bg1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514981
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 255, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bg1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bg1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.2', 'subgroup_hash': 2, 'subgroup_order': 8, 'subgroup_tex': 'C_2\\times C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514982
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 256, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514983
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 257, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514984
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 258, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514985
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 259, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514987
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 260, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514988
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 261, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.96.bh2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '96.bh2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 96, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '8.5', 'subgroup_hash': 5, 'subgroup_order': 8, 'subgroup_tex': 'C_2^3', 'supersolvable': True, 'sylow': 0}
-
id: 68514989
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 2, 'counter': 262, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.128.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '128.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 128, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
-
id: 68514990
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': True, 'core_order': 4, 'counter': 263, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '768.1088652.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.1495', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1495, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^3.S_4', 'simple': False, 'solvable': True, 'special_labels': ['D3', 'C5'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514991
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 2, 'counter': 264, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514992
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 265, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514993
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 2, 'counter': 266, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.c1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.c1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514994
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 2, 'counter': 267, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68514995
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 128, 'characteristic': False, 'core_order': 1, 'counter': 268, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514996
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 269, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.f1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514998
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 270, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.f1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68514999
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 271, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.f2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515000
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 272, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.f2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.f2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515001
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 273, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515002
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 274, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.g1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515003
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 275, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.g2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515004
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 276, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.g2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.g2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515005
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 277, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.h1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.h1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515006
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 278, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.i1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.i1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515007
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 279, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.j1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.j1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515009
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 280, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.k1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.k1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515010
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 281, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.l1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515011
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 282, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.l1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515012
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 283, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.l2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515013
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 284, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.l2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.l2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515014
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 285, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.m1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.m1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515015
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 286, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515016
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 287, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515017
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 288, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515018
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 289, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515020
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 290, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515021
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 291, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.n2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.n2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515022
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 292, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515023
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 293, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515024
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 294, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o2.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o2.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515025
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 295, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o2.a2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o2.a2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515026
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 296, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o2.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o2.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515027
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': False, 'core_order': 1, 'counter': 297, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '768.1088652.192.o2.b2', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.o2.b2', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.2', 'subgroup_hash': 2, 'subgroup_order': 4, 'subgroup_tex': 'C_2^2', 'supersolvable': True, 'sylow': 0}
-
id: 68515028
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 298, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.p1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.p1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515029
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 16, 'characteristic': False, 'core_order': 1, 'counter': 299, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.192.p1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '192.p1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 192, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '4.1', 'subgroup_hash': 1, 'subgroup_order': 4, 'subgroup_tex': 'C_4', 'supersolvable': True, 'sylow': 0}
-
id: 68515032
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': False, 'core_order': 1, 'counter': 300, 'cyclic': True, 'direct': None, 'hall': 3, 'label': '768.1088652.256.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '256.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 256, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 3}
-
id: 68515033
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 2, 'counter': 301, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '768.1088652.384.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '384.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '384.18135', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 18135, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 384, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_4^2:S_4', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515034
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 302, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515035
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 256, 'characteristic': False, 'core_order': 1, 'counter': 303, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.c1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.c1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515036
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 304, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.d1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515037
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 305, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.d1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.d1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515038
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 306, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.e1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515039
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 64, 'characteristic': False, 'core_order': 1, 'counter': 307, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '768.1088652.384.e1.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': False, 'nilpotent': True, 'normal': False, 'old_label': '384.e1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 384, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': True, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
-
id: 68515040
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '768.1088652', 'ambient_counter': 1088652, 'ambient_order': 768, 'ambient_tex': 'C_2^5.S_4', 'central': True, 'central_factor': False, 'centralizer_order': 768, 'characteristic': True, 'core_order': 1, 'counter': 308, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '768.1088652.768.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '768.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '768.1088652', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1088652, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 768, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_2^5.S_4', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U1', 'D4', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
-
gps_subgroup_data • Show schema
Hide schema
-
id: 68514846
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.p1.a1'], 'contains': ['96.c1.a1', '96.e1.a1', '96.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3213, -1, 7179, -1, 8608, -1, 5723, -1], 'generators': [1, 240], 'label': '768.1088652.48.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514847
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.l1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.g1.a1', '24.p1.a1'], 'contains': ['96.c1.a1', '96.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3504, -1, 5638, -1, 7835, -1, 4878, -1], 'generators': [1, 624], 'label': '768.1088652.48.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.l1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514848
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.m1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.h1.a1', '24.p1.a1'], 'contains': ['96.c1.a1', '96.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4030, -1, 5572, -1, 7981, -1, 4706, -1], 'generators': [385, 624], 'label': '768.1088652.48.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '48.m1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.m1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514849
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.n1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '24.q1.a1'], 'contains': ['96.c1.a1', '96.y1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9643, -1, 5419, -1, 6237, -1, 302, -1], 'generators': [577, 240], 'label': '768.1088652.48.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.n1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514905
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1'], 'contains': ['96.bf1.a1', '96.bg1.a1', '96.bh2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1026, -1, 9338, -1, 9925, -1, 8358, -1], 'generators': [385, 24], 'label': '768.1088652.48.bv1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '48.bv1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514906
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.a1'], 'contains': ['96.bf1.a1', '96.bg1.a1', '96.bh2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1026, -1, 9419, -1, 9925, -1, 8551, -1], 'generators': [385, 408], 'label': '768.1088652.48.bv1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '48.bv1.a2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514907
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1'], 'contains': ['96.bf1.b1', '96.bg1.b1', '96.bh2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1026, -1, 7972, -1, 9925, -1, 6736, -1], 'generators': [385, 600], 'label': '768.1088652.48.bv1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '48.bv1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514926
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.j1.a1', '48.q1.a1'], 'contains': ['192.b1.a1', '192.j1.a1', '192.k1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7760, -1, 4275, -1, 5081, -1, 2643, -1], 'generators': [2, 648], 'label': '768.1088652.96.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.d1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515058
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['32.b2.b1', '48.s1.b1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [240, -1, 8833, -1, 9650, -1, 8936, -1], 'generators': [1, 312, 2, 4, 732], 'label': '768.1088652.16.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '16.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515059
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1'], 'contains': ['32.b2.b2', '48.s1.b2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [240, -1, 8899, -1, 9650, -1, 9080, -1], 'generators': [1, 696, 2, 4, 252], 'label': '768.1088652.16.b1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '16.b1.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514827
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '16.b1.b2'], 'contains': ['64.c2.b2', '96.i2.b2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [76, -1, 8603, -1, 7526, -1, 9133, -1], 'generators': [2, 4, 252, 696], 'label': '768.1088652.32.b2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '32.b2.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514808
{'ambient': '768.1088652', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '384.a1.a1', 'complements': ['768.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '4.b1.a1', '4.b1.b1', '4.c1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3923, 3292, 6206, 4167, 5316, 3876, 6682, 3762], 'generators': [1, 384, 24, 624, 2, 12, 480, 576, 4], 'label': '768.1088652.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68514809
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530058', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.e1.b1', '12.g1.a1', '12.q1.a1', '12.r1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5017, -1, 6529, -1, 5397, -1, 5380, -1], 'generators': [25, 12, 576], 'label': '768.1088652.6.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.c1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514810
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.o1.a1', '12.p1.b1'], 'contains': ['48.a1.a1', '48.z1.a1', '48.ba1.a1', '48.bd1.a1', '48.bf1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4041, -1, 5025, -1, 4798, -1, 3675, -1], 'generators': [626, 12, 24], 'label': '768.1088652.24.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bf1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514811
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.o1.b1', '12.p1.a1'], 'contains': ['48.a1.b1', '48.z1.b1', '48.ba1.b1', '48.bd1.b1', '48.bf1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4041, -1, 4328, -1, 4798, -1, 4828, -1], 'generators': [626, 636, 600], 'label': '768.1088652.24.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bf1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514812
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.i1.a1', '12.p1.a1'], 'contains': ['48.a1.b1', '48.bc1.b1', '48.be1.b1', '48.bg1.a1', '48.bh1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4282, -1, 2799, -1, 3401, -1, 5000, -1], 'generators': [12, 600, 624], 'label': '768.1088652.24.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514813
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bg1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.i1.b1', '12.p1.b1'], 'contains': ['48.a1.a1', '48.bc1.a1', '48.be1.a1', '48.bg1.a1', '48.bh1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4282, -1, 3686, -1, 3401, -1, 5171, -1], 'generators': [12, 24, 624], 'label': '768.1088652.24.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bg1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514814
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bh1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.q1.a1'], 'contains': ['48.bj1.a1', '48.bj1.b1', '48.bm1.a1', '48.bo1.a1', '48.bp1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7728, -1, 3341, -1, 1973, -1, 950, -1], 'generators': [14, 588, 624], 'label': '768.1088652.24.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bh1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514815
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.bi1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.bi1.a1', '48.bi1.b1', '48.bk1.a1', '48.bk1.b1', '48.bn1.a1', '48.bp1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6750, -1, 742, -1, 955, -1, 1954, -1], 'generators': [26, 588, 624], 'label': '768.1088652.24.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bi1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514816
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.q1.a1', '12.r1.a1'], 'contains': ['48.bl1.a1', '48.bm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3100, -1, 6735, -1, 5926, -1, 5624, -1], 'generators': [601, 624], 'label': '768.1088652.24.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bj1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68514817
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.q1.a1', '12.r1.a1'], 'contains': ['48.bl1.b1', '48.bm1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3100, -1, 6816, -1, 5926, -1, 6021, -1], 'generators': [25, 624], 'label': '768.1088652.24.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '24.bj1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68514818
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bk1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.n1.a1', '12.r1.a1'], 'contains': ['48.b1.a1', '48.bi1.a1', '48.bi1.b1', '48.bm1.a1', '48.bq1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6543, -1, 2960, -1, 1683, -1, 1131, -1], 'generators': [14, 624, 576], 'label': '768.1088652.24.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bk1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514819
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.bl1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1'], 'contains': ['48.bj1.a1', '48.bj1.b1', '48.bk1.a1', '48.bk1.b1', '48.bn1.a1', '48.br1.a1', '48.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7295, -1, 1198, -1, 1101, -1, 1682, -1], 'generators': [626, 588, 456], 'label': '768.1088652.24.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bl1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514820
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.b1', '12.d1.a1', '12.e1.a1', '12.h1.b1', '12.i1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [2983, -1, 6699, -1, 7194, -1, 5788, -1], 'generators': [1, 600, 624], 'label': '768.1088652.6.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514821
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '32.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1', '16.a1.a1'], 'contains': ['64.b1.a1', '96.a1.a1', '128.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1410, -1, 6839, -1, 6573, -1, 7783, -1], 'generators': [2, 4, 480, 384], 'label': '768.1088652.32.a1.a1', 'mobius_quo': None, 'mobius_sub': -2, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '32.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514822
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1'], 'contains': ['64.c1.a1', '96.i1.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [398, -1, 8782, -1, 7312, -1, 9677, -1], 'generators': [2, 4, 396, 120], 'label': '768.1088652.32.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.a1', 'old_label': '32.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68514823
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1'], 'contains': ['64.c1.b1', '96.i1.b1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [398, -1, 7290, -1, 7312, -1, 8792, -1], 'generators': [2, 4, 348, 216], 'label': '768.1088652.32.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.b1', 'old_label': '32.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68514824
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a1'], 'contains': ['64.c2.a1', '96.i2.a1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [76, -1, 9793, -1, 7526, -1, 9809, -1], 'generators': [2, 4, 12, 24], 'label': '768.1088652.32.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '32.b2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514825
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '16.b1.a2'], 'contains': ['64.c2.a2', '96.i2.a2', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [76, -1, 9097, -1, 7526, -1, 9943, -1], 'generators': [2, 4, 492, 408], 'label': '768.1088652.32.b2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '32.b2.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514826
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '32.b2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '16.b1.b1'], 'contains': ['64.c2.b1', '96.i2.b1', '128.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [76, -1, 8468, -1, 7526, -1, 9001, -1], 'generators': [2, 4, 732, 312], 'label': '768.1088652.32.b2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '32.b2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32.b2.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514828
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': ['16.b1.b2', '16.b1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '24.a1.a1', '24.bf1.a1', '24.bg1.b1'], 'contains': ['96.r1.a1', '96.z1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2601, 4300, 6154, 5735, 5313, 3361, 5997, 3448], 'generators': [12, 24, 480, 384], 'label': '768.1088652.48.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': ['12.a1.a1', '24.a1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514829
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.b1', 'complements': ['16.b1.a1', '16.b1.a2'], 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '24.a1.b1', '24.bf1.b1', '24.bg1.a1'], 'contains': ['96.r1.b1', '96.z1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [2601, 4300, 5157, 2794, 5313, 3361, 5804, 1837], 'generators': [636, 600, 480, 384], 'label': '768.1088652.48.a1.b1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': ['12.a1.a1', '24.a1.b1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.a1.b1', 'projective_image': '768.1088652', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514830
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '48.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': ['16.b1.a1', '16.b1.a2', '16.b1.b1', '16.b1.b2'], 'conjugacy_class_count': 1, 'contained_in': ['16.d1.a1', '24.b1.a1', '24.bd1.a1', '24.bk1.a1'], 'contains': ['96.bb1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6628, 2420, 478, 784, 514, 5281, 1420, 5059], 'generators': [624, 576], 'label': '768.1088652.48.b1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': ['12.a1.a1', '24.b1.a1'], 'normal_contains': ['192.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '48.b1.a1', 'projective_image': '768.1088652', 'quotient_action_image': '24.12', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '48.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514831
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.d1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.b1.a1', '12.d1.a1', '12.e1.b1', '12.h1.a1', '12.i1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2983, -1, 6935, -1, 7194, -1, 6026, -1], 'generators': [1, 24, 624], 'label': '768.1088652.6.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.d1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.d1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514832
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.k1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '96.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2475, -1, 7557, -1, 8823, -1, 6470, -1], 'generators': [1, 396], 'label': '768.1088652.48.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514833
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.c1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.k1.b1'], 'contains': ['96.b1.b1', '96.e1.a1', '96.f1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2475, -1, 7476, -1, 8823, -1, 6093, -1], 'generators': [1, 348], 'label': '768.1088652.48.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.c1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.c1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514834
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.a1', '24.k1.a1'], 'contains': ['96.b1.a1', '96.e1.a1', '96.g1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1517, -1, 8398, -1, 9037, -1, 7639, -1], 'generators': [1, 12, 480], 'label': '768.1088652.48.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514835
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.d1.a1', '24.e1.b1', '24.k1.b1'], 'contains': ['96.b1.b1', '96.e1.a1', '96.g1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1517, -1, 7875, -1, 9037, -1, 7485, -1], 'generators': [1, 732, 480], 'label': '768.1088652.48.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.d1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.d1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514836
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.a1', '24.k1.a1'], 'contains': ['96.b1.a1', '96.f1.a1', '96.bf1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2154, -1, 8286, -1, 9533, -1, 7173, -1], 'generators': [385, 12, 480], 'label': '768.1088652.48.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '48.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514837
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.f1.b1', '24.k1.b1'], 'contains': ['96.b1.b1', '96.f1.a1', '96.bf1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2154, -1, 7351, -1, 9533, -1, 6338, -1], 'generators': [385, 732, 480], 'label': '768.1088652.48.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '48.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514838
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.a1', '24.f1.a1', '24.l1.a1'], 'contains': ['96.b1.a1', '96.h1.a1', '96.s1.b1', '96.bg1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1315, -1, 9155, -1, 9285, -1, 7926, -1], 'generators': [25, 12, 480], 'label': '768.1088652.48.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514839
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.e1.b1', '24.f1.b1', '24.l1.b1'], 'contains': ['96.b1.b1', '96.h1.b1', '96.s1.a1', '96.bg1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1315, -1, 7762, -1, 9285, -1, 6603, -1], 'generators': [601, 732, 480], 'label': '768.1088652.48.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.f1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.f1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514840
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.c1.a1', '24.d1.a1', '24.m1.a1'], 'contains': ['96.b1.a1', '96.b1.b1', '96.c1.a1', '96.m1.a1', '96.m1.b1', '96.p1.a1', '96.t1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3355, -1, 6813, -1, 7097, -1, 4991, -1], 'generators': [2, 12, 624], 'label': '768.1088652.48.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.g1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514841
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.h1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1'], 'contains': ['96.b2.a1', '96.b2.b1', '96.d1.a1', '96.n1.a1', '96.n1.b1', '96.q1.a1', '96.u1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5149, -1, 5775, -1, 5645, -1, 5261, -1], 'generators': [2, 12, 600], 'label': '768.1088652.48.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '48.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.h1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514842
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.b1', '12.f1.a1', '12.i1.a1', '12.l1.b1', '12.o1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4607, -1, 6037, -1, 6057, -1, 4617, -1], 'generators': [577, 600, 624], 'label': '768.1088652.6.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514843
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.e1.a1', '24.f1.a1'], 'contains': ['96.b1.a1', '96.b2.a1', '96.i1.a1', '96.i2.a1', '96.i2.a2', '96.o1.a1', '96.o2.a1', '96.r1.a1', '96.bh1.a1', '96.bh2.a1', '96.bh2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1158, -1, 9241, -1, 8299, -1, 8647, -1], 'generators': [2, 12, 24, 480], 'label': '768.1088652.48.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514844
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.i1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.e1.b1', '24.f1.b1'], 'contains': ['96.b1.b1', '96.b2.b1', '96.i1.b1', '96.i2.b1', '96.i2.b2', '96.o1.b1', '96.o2.b1', '96.r1.b1', '96.bh1.b1', '96.bh2.b1', '96.bh2.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1158, -1, 7266, -1, 8299, -1, 7292, -1], 'generators': [2, 636, 600, 480], 'label': '768.1088652.48.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.i1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514845
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.g1.a1', '24.h1.a1', '24.o1.a1'], 'contains': ['96.c1.a1', '96.d1.a1', '96.v1.a1', '96.w1.a1', '96.x1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8682, -1, 4405, -1, 4328, -1, 670, -1], 'generators': [2, 300, 624], 'label': '768.1088652.48.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.j1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514850
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.i1.a1', '24.j1.a1', '24.k1.a1', '24.l1.a1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.a1.a1', '96.b1.a1', '96.b2.a1', '96.j1.a1', '96.j2.a1', '96.z1.a1', '96.ba1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3107, -1, 6237, -1, 6745, -1, 5643, -1], 'generators': [2, 12, 480, 384], 'label': '768.1088652.48.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.o1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514851
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '48.o1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.i1.b1', '24.j1.b1', '24.k1.b1', '24.l1.b1', '24.m1.a1', '24.n1.a1'], 'contains': ['96.a1.a1', '96.b1.b1', '96.b2.b1', '96.j1.b1', '96.j2.b1', '96.z1.b1', '96.ba1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3107, -1, 6070, -1, 6745, -1, 5450, -1], 'generators': [2, 636, 480, 384], 'label': '768.1088652.48.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.o1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.o1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514852
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '48.p1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.i1.a1', '24.i1.b1', '24.m1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1'], 'contains': ['96.a1.a1', '96.c1.a1', '96.k1.a1', '96.bb1.a1', '96.bc1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7195, -1, 4831, -1, 4561, -1, 1032, -1], 'generators': [2, 624, 384], 'label': '768.1088652.48.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.p1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.p1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514853
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.53380', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.e1.a1', '12.f1.a1', '12.i1.b1', '12.l1.a1', '12.o1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4607, -1, 6206, -1, 6057, -1, 4253, -1], 'generators': [577, 24, 624], 'label': '768.1088652.6.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.e1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514854
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '48.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.i1.b1', '24.j1.a1', '24.j1.b1', '24.n1.a1', '24.o1.a1', '24.r1.a1'], 'contains': ['96.a1.a1', '96.d1.a1', '96.l1.a1', '96.bd1.a1', '96.be1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7853, -1, 4300, -1, 3268, -1, 2509, -1], 'generators': [2, 648, 480], 'label': '768.1088652.48.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.q1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514855
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.r1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '48.g1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '24.k1.a1', '24.k1.b1', '24.p1.a1'], 'contains': ['96.a1.a1', '96.e1.a1', '96.f1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2874, -1, 7638, -1, 8453, -1, 6205, -1], 'generators': [1, 384], 'label': '768.1088652.48.r1.a1', 'mobius_quo': None, 'mobius_sub': -8, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.r1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.r1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514856
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a1', '24.e1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.i2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [801, -1, 9746, -1, 9746, -1, 9255, -1], 'generators': [1, 24], 'label': '768.1088652.48.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.s1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514857
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.a2', '24.e1.a1'], 'contains': ['96.g1.a1', '96.h1.a1', '96.i2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [801, -1, 9637, -1, 9746, -1, 9366, -1], 'generators': [1, 408], 'label': '768.1088652.48.s1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '48.s1.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.a2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514858
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b1', '24.e1.b1'], 'contains': ['96.g1.b1', '96.h1.b1', '96.i2.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [801, -1, 8550, -1, 9746, -1, 8135, -1], 'generators': [1, 216], 'label': '768.1088652.48.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.s1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514859
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.s1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.b1.b2', '24.e1.b1'], 'contains': ['96.g1.b1', '96.h1.b1', '96.i2.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [801, -1, 8631, -1, 9746, -1, 8247, -1], 'generators': [1, 600], 'label': '768.1088652.48.s1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '48.s1.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.s1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514860
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1'], 'contains': ['96.j1.a1', '96.s1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2329, -1, 8133, -1, 8144, -1, 7040, -1], 'generators': [25, 396], 'label': '768.1088652.48.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.a1', 'old_label': '48.t1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514861
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '48.t1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1'], 'contains': ['96.j1.b1', '96.s1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2329, -1, 6903, -1, 8144, -1, 5546, -1], 'generators': [601, 348], 'label': '768.1088652.48.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.b1.b1', 'old_label': '48.t1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.t1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514862
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1'], 'contains': ['96.j1.a1', '96.j1.b1', '96.k1.a1', '96.m1.a1', '96.m1.b1', '96.p1.a1', '96.t1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3741, -1, 5971, -1, 6021, -1, 4593, -1], 'generators': [386, 12, 624], 'label': '768.1088652.48.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '48.u1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.u1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68514863
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.v1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1'], 'contains': ['96.j2.a1', '96.j2.b1', '96.l1.a1', '96.n1.a1', '96.n1.b1', '96.q1.a1', '96.u1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5393, -1, 5873, -1, 5010, -1, 5126, -1], 'generators': [386, 12, 600], 'label': '768.1088652.48.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '48.v1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.v1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514864
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.a1'], 'contains': ['16.c1.a1', '24.a1.a1', '32.a1.a1', '32.b1.a1', '32.b2.a1', '32.b2.a2'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1122, -1, 8619, -1, 6705, -1, 9388, -1], 'generators': [2, 384, 480, 4, 36, 24], 'label': '768.1088652.8.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '8.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68514865
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1'], 'contains': ['96.j1.a1', '96.j2.a1', '96.o1.a1', '96.o2.a1', '96.r1.a1', '96.bh1.a1', '96.bh2.a1', '96.bh2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1673, -1, 8755, -1, 7698, -1, 8454, -1], 'generators': [386, 12, 24, 480], 'label': '768.1088652.48.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '48.w1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514866
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.w1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1'], 'contains': ['96.j1.b1', '96.j2.b1', '96.o1.b1', '96.o2.b1', '96.r1.b1', '96.bh1.b1', '96.bh2.b1', '96.bh2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1673, -1, 7000, -1, 7698, -1, 6944, -1], 'generators': [386, 636, 600, 480], 'label': '768.1088652.48.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '48.w1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.w1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514867
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1'], 'contains': ['96.k1.a1', '96.l1.a1', '96.v1.a1', '96.w1.a1', '96.x1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8504, -1, 3956, -1, 2602, -1, 536, -1], 'generators': [386, 300, 624], 'label': '768.1088652.48.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '48.x1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.x1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514868
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.y1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1'], 'contains': ['96.k1.a1', '96.y1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9924, -1, 5329, -1, 5833, -1, 186, -1], 'generators': [577, 624], 'label': '768.1088652.48.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.k1.a1', 'old_label': '48.y1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.y1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514927
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.e1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.b1', '48.d1.a1', '48.d1.b1', '48.k1.a1', '48.l1.a1', '48.r1.a1'], 'contains': ['192.b1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2685, -1, 7712, -1, 8472, -1, 6700, -1], 'generators': [1, 480], 'label': '768.1088652.96.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514869
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.s1.a1', '24.v1.a1', '24.w1.a1', '24.y1.a1', '24.ba1.a1', '24.bf1.a1'], 'contains': ['96.m1.a1', '96.z1.a1', '96.ba1.a1', '96.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4178, -1, 5244, -1, 4793, -1, 3204, -1], 'generators': [626, 12, 384], 'label': '768.1088652.48.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.z1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514870
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.s1.b1', '24.v1.b1', '24.w1.b1', '24.y1.b1', '24.ba1.b1', '24.bf1.b1'], 'contains': ['96.m1.b1', '96.z1.b1', '96.ba1.b1', '96.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4178, -1, 5061, -1, 4793, -1, 4212, -1], 'generators': [626, 636, 384], 'label': '768.1088652.48.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.z1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.z1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514871
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.t1.a1', '24.u1.a1', '24.x1.a1', '24.z1.a1', '24.ba1.a1', '24.bf1.a1'], 'contains': ['96.n1.a1', '96.z1.a1', '96.ba1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4713, -1, 3857, -1, 3895, -1, 2958, -1], 'generators': [602, 12, 384], 'label': '768.1088652.48.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.ba1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514872
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.t1.b1', '24.u1.b1', '24.x1.b1', '24.z1.b1', '24.ba1.b1', '24.bf1.b1'], 'contains': ['96.n1.b1', '96.z1.b1', '96.ba1.b1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4713, -1, 2637, -1, 3895, -1, 3943, -1], 'generators': [26, 636, 384], 'label': '768.1088652.48.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.ba1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514873
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '24.x1.a1', '24.y1.a1', '24.z1.b1', '24.ba1.b1'], 'contains': ['96.o1.a1', '96.o2.a1', '96.z1.a1', '96.ba1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3001, -1, 4584, -1, 5183, -1, 5369, -1], 'generators': [26, 12, 480, 384], 'label': '768.1088652.48.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bb1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514874
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '48.bb1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.a1.b1', '24.x1.b1', '24.y1.b1', '24.z1.a1', '24.ba1.a1'], 'contains': ['96.o1.b1', '96.o2.b1', '96.z1.b1', '96.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3001, -1, 4526, -1, 5183, -1, 4792, -1], 'generators': [602, 636, 480, 384], 'label': '768.1088652.48.bb1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bb1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bb1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514875
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '8.a1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.b1.b1'], 'contains': ['16.c1.b1', '24.a1.b1', '32.a1.a1', '32.b1.b1', '32.b2.b1', '32.b2.b2'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1122, -1, 7266, -1, 6705, -1, 8312, -1], 'generators': [2, 384, 480, 4, 468, 216], 'label': '768.1088652.8.a1.b1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '8.a1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.a1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68514876
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.a1', '24.t1.a1', '24.x1.a1', '24.bc1.a1', '24.bd1.a1', '24.bg1.b1'], 'contains': ['96.z1.a1', '96.bb1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6028, -1, 1603, -1, 1102, -1, 2265, -1], 'generators': [12, 576], 'label': '768.1088652.48.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bc1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514877
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bc1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.b1', '24.t1.b1', '24.x1.b1', '24.bc1.a1', '24.bd1.a1', '24.bg1.a1'], 'contains': ['96.z1.b1', '96.bb1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6028, -1, 976, -1, 1102, -1, 2376, -1], 'generators': [636, 576], 'label': '768.1088652.48.bc1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bc1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bc1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514878
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.a1', '24.u1.a1', '24.ba1.b1', '24.bb1.a1', '24.be1.a1', '24.bf1.a1'], 'contains': ['96.z1.a1', '96.bc1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7679, -1, 3427, -1, 2165, -1, 1738, -1], 'generators': [578, 12], 'label': '768.1088652.48.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bd1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514879
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bd1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.b1', '24.u1.b1', '24.ba1.a1', '24.bb1.a1', '24.be1.a1', '24.bf1.b1'], 'contains': ['96.z1.b1', '96.bc1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7679, -1, 3068, -1, 2165, -1, 1961, -1], 'generators': [578, 636], 'label': '768.1088652.48.bd1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bd1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bd1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514880
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.u1.a1', '24.y1.a1', '24.bc1.a1', '24.bg1.b1'], 'contains': ['96.z1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5560, -1, 3767, -1, 2343, -1, 3685, -1], 'generators': [12, 648], 'label': '768.1088652.48.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.be1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514881
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.u1.b1', '24.y1.b1', '24.bc1.a1', '24.bg1.a1'], 'contains': ['96.z1.b1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5560, -1, 2373, -1, 2343, -1, 3573, -1], 'generators': [636, 456], 'label': '768.1088652.48.be1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.be1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.be1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514882
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.t1.a1', '24.z1.b1', '24.be1.a1', '24.bf1.a1'], 'contains': ['96.z1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5706, -1, 3345, -1, 3481, -1, 3462, -1], 'generators': [650, 12], 'label': '768.1088652.48.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bf1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514883
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bf1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.t1.b1', '24.z1.a1', '24.be1.a1', '24.bf1.b1'], 'contains': ['96.z1.b1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5706, -1, 3606, -1, 3481, -1, 3081, -1], 'generators': [458, 636], 'label': '768.1088652.48.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bf1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514884
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bg1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.z1.a1', '24.z1.b1', '24.bb1.a1', '24.bd1.a1', '24.bg1.a1', '24.bg1.b1'], 'contains': ['96.p1.a1', '96.z1.a1', '96.z1.b1', '96.bb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4355, -1, 3516, -1, 3679, -1, 4077, -1], 'generators': [12, 624, 384], 'label': '768.1088652.48.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bg1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514885
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bh1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.ba1.a1', '24.ba1.b1', '24.bc1.a1', '24.be1.a1', '24.bg1.a1', '24.bg1.b1'], 'contains': ['96.q1.a1', '96.z1.a1', '96.z1.b1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4940, -1, 3256, -1, 2819, -1, 4347, -1], 'generators': [12, 600, 384], 'label': '768.1088652.48.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bh1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514886
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '8.b1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '4.c1.a1'], 'contains': ['16.d1.a1', '24.b1.a1', '32.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3668, -1, 1891, -1, 2176, -1, 6463, -1], 'generators': [2, 384, 96, 4, 48, 192], 'label': '768.1088652.8.b1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '8.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68514887
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.a1', '24.t1.a1', '24.x1.b1', '24.z1.a1', '24.bi1.a1', '24.bk1.a1'], 'contains': ['96.ba1.a1', '96.bb1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6285, -1, 2140, -1, 1676, -1, 1627, -1], 'generators': [602, 624], 'label': '768.1088652.48.bi1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bi1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514888
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bi1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.b1', '24.t1.b1', '24.x1.a1', '24.z1.b1', '24.bi1.a1', '24.bk1.a1'], 'contains': ['96.ba1.b1', '96.bb1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6285, -1, 1991, -1, 1676, -1, 2072, -1], 'generators': [26, 624], 'label': '768.1088652.48.bi1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bi1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bi1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514889
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.b1', '24.s1.a1', '24.u1.a1', '24.y1.b1', '24.ba1.a1', '24.bh1.a1', '24.bl1.a1'], 'contains': ['96.ba1.a1', '96.bc1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7021, -1, 3687, -1, 1986, -1, 1516, -1], 'generators': [434, 648], 'label': '768.1088652.48.bj1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bj1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514890
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bj1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.i1.a1', '24.s1.b1', '24.u1.b1', '24.y1.a1', '24.ba1.b1', '24.bh1.a1', '24.bl1.a1'], 'contains': ['96.ba1.b1', '96.bc1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7021, -1, 2502, -1, 1986, -1, 1850, -1], 'generators': [626, 648], 'label': '768.1088652.48.bj1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bj1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bj1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514891
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.b1', '24.t1.a1', '24.u1.a1', '24.x1.b1', '24.ba1.a1', '24.bi1.a1', '24.bl1.a1'], 'contains': ['96.ba1.a1', '96.bd1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6466, -1, 1684, -1, 1281, -1, 2642, -1], 'generators': [590, 648], 'label': '768.1088652.48.bk1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bk1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514892
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bk1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.j1.a1', '24.t1.b1', '24.u1.b1', '24.x1.a1', '24.ba1.b1', '24.bi1.a1', '24.bl1.a1'], 'contains': ['96.ba1.b1', '96.bd1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6466, -1, 1244, -1, 1281, -1, 2753, -1], 'generators': [14, 648], 'label': '768.1088652.48.bk1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bk1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bk1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514893
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.b1', '24.v1.a1', '24.bj1.a1'], 'contains': ['96.s1.a1', '96.ba1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2728, -1, 6586, -1, 6900, -1, 4470, -1], 'generators': [601, 384], 'label': '768.1088652.48.bl1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.a1', 'old_label': '48.bl1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514894
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '48.bl1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.l1.a1', '24.v1.b1', '24.bj1.b1'], 'contains': ['96.s1.b1', '96.ba1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2728, -1, 6696, -1, 6900, -1, 5900, -1], 'generators': [25, 384], 'label': '768.1088652.48.bl1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.e1.b1', 'old_label': '48.bl1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bl1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514895
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bm1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.m1.a1', '24.x1.a1', '24.x1.b1', '24.bh1.a1', '24.bj1.a1', '24.bj1.b1', '24.bk1.a1'], 'contains': ['96.t1.a1', '96.ba1.a1', '96.ba1.b1', '96.bb1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4535, -1, 4054, -1, 4112, -1, 3808, -1], 'generators': [14, 624, 384], 'label': '768.1088652.48.bm1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bm1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bm1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514896
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bn1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.n1.a1', '24.x1.a1', '24.x1.b1', '24.y1.a1', '24.y1.b1', '24.bi1.a1', '24.bl1.a1'], 'contains': ['96.u1.a1', '96.ba1.a1', '96.ba1.b1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5867, -1, 3158, -1, 3035, -1, 3339, -1], 'generators': [638, 648, 480], 'label': '768.1088652.48.bn1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bn1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bn1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514897
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '8.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['16.e1.a1', '24.r1.a1', '32.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [4009, -1, 2025, -1, 442, -1, 6722, -1], 'generators': [2, 384, 96, 4, 276, 552], 'label': '768.1088652.8.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '8.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.c1.a1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
-
id: 68514898
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '48.bo1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.b1.a1', '24.s1.a1', '24.s1.b1', '24.bb1.a1', '24.bh1.a1'], 'contains': ['96.bb1.a1', '96.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8009, -1, 2774, -1, 1831, -1, 779, -1], 'generators': [578, 624], 'label': '768.1088652.48.bo1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bo1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bo1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514899
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bp1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.bc1.a1', '24.bd1.a1', '24.bh1.a1', '24.bi1.a1'], 'contains': ['96.v1.a1', '96.bb1.a1', '96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7410, -1, 557, -1, 688, -1, 1311, -1], 'generators': [588, 624, 384], 'label': '768.1088652.48.bp1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bp1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bp1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514900
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bq1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.t1.a1', '24.t1.b1', '24.bb1.a1', '24.bk1.a1'], 'contains': ['96.w1.a1', '96.bb1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [8151, -1, 2283, -1, 1479, -1, 887, -1], 'generators': [590, 624, 384], 'label': '768.1088652.48.bq1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '48.bq1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bq1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514901
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.br1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.o1.a1', '24.s1.a1', '24.s1.b1', '24.u1.a1', '24.u1.b1', '24.be1.a1', '24.bl1.a1'], 'contains': ['96.x1.a1', '96.bc1.a1', '96.bd1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [8327, -1, 1772, -1, 905, -1, 1176, -1], 'generators': [578, 648, 480], 'label': '768.1088652.48.br1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.br1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.br1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514902
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bs1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.11', 'aut_weyl_index': 384, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.q1.a1', '24.w1.a1', '24.w1.b1'], 'contains': ['96.y1.a1', '96.bc1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9795, -1, 5503, -1, 5457, -1, 418, -1], 'generators': [577, 384], 'label': '768.1088652.48.bs1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.f1.a1', 'old_label': '48.bs1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bs1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514903
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bt1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.r1.a1', '24.t1.a1', '24.t1.b1', '24.u1.a1', '24.u1.b1', '24.be1.a1', '24.bi1.a1'], 'contains': ['96.bd1.a1', '96.be1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7552, -1, 636, -1, 385, -1, 2169, -1], 'generators': [446, 648], 'label': '768.1088652.48.bt1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '48.bt1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bt1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514904
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '48.bu1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.e1.a1', '24.r1.a1', '24.bc1.a1', '24.bl1.a1'], 'contains': ['96.bd1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6824, -1, 23, -1, 255, -1, 2850, -1], 'generators': [588, 456], 'label': '768.1088652.48.bu1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '48.bu1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bu1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68514908
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 8, 'centralizer': '96.a1.a1', 'complements': ['64.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['24.bc1.a1', '24.bd1.a1', '24.bg1.a1', '24.bg1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5627, 2145, 2142, 2476, 881, 2190, 3926, 1837], 'generators': [12, 24, 624, 576], 'label': '768.1088652.12.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['4.a1.a1', '6.a1.a1'], 'normal_contains': ['48.a1.a1', '48.a1.b1', '48.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': '6.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68514909
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '48.bv1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '8.5', 'aut_weyl_index': 768, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.f1.b1'], 'contains': ['96.bf1.b1', '96.bg1.b1', '96.bh2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1026, -1, 8053, -1, 9925, -1, 6847, -1], 'generators': [385, 216], 'label': '768.1088652.48.bv1.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '48.bv1.b2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.bv1.b2', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514910
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '64.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '12.4', 'aut_weyl_index': 512, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.a1.a1', '16.b1.a1', '16.b1.a2', '16.b1.b1', '16.b1.b2'], 'contains': ['128.a1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [281, -1, 9909, -1, 8868, -1, 9555, -1], 'generators': [1, 2, 4], 'label': '768.1088652.64.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '64.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514911
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '64.b1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '16.c1.b1', '16.d1.a1', '16.e1.a1', '32.a1.a1'], 'contains': ['192.a1.a1', '256.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [2123, -1, 4713, -1, 1822, -1, 7340, -1], 'generators': [4, 480, 384], 'label': '768.1088652.64.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '64.b1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514912
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b1.a1'], 'contains': ['192.o1.a1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [440, -1, 8132, -1, 6373, -1, 9710, -1], 'generators': [4, 396, 120], 'label': '768.1088652.64.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.a1', 'old_label': '64.c1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68514913
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b1.b1'], 'contains': ['192.o1.b1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 32, 'diagramx': [440, -1, 6344, -1, 6373, -1, 8672, -1], 'generators': [4, 348, 216], 'label': '768.1088652.64.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '32.b1.b1', 'old_label': '64.c1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c1.b1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68514914
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b2.a1'], 'contains': ['192.o2.a1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [103, -1, 8890, -1, 6487, -1, 9796, -1], 'generators': [4, 12, 24], 'label': '768.1088652.64.c2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '64.c2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514915
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.a1', '32.b2.a2'], 'contains': ['192.o2.a2', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [103, -1, 8647, -1, 6487, -1, 9933, -1], 'generators': [4, 492, 408], 'label': '768.1088652.64.c2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '64.c2.a2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514916
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b2.b1'], 'contains': ['192.o2.b1', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [103, -1, 6614, -1, 6487, -1, 8743, -1], 'generators': [4, 732, 312], 'label': '768.1088652.64.c2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b1', 'old_label': '64.c2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514917
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '64.c2', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '24.12', 'aut_weyl_index': 256, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['16.c1.b1', '32.b2.b2'], 'contains': ['192.o2.b2', '256.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [103, -1, 6692, -1, 6487, -1, 8814, -1], 'generators': [4, 252, 696], 'label': '768.1088652.64.c2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.b2', 'old_label': '64.c2.b2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '64.c2.b2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68514918
{'ambient': '768.1088652', 'aut_centralizer_order': 1024, 'aut_label': '96.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '48.o1.a1', '48.o1.b1', '48.p1.a1', '48.q1.a1', '48.r1.a1'], 'contains': ['192.a1.a1', '192.b1.a1', '192.e1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4646, 5677, 5628, 6201, 5923, 7201, 5330, 6670], 'generators': [2, 480, 384], 'label': '768.1088652.96.a1.a1', 'mobius_quo': 1, 'mobius_sub': 96, 'normal_closure': '96.a1.a1', 'normal_contained_in': ['24.a1.a1', '24.a1.b1', '24.b1.a1'], 'normal_contains': ['192.a1.a1', '384.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '96.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '6.1', 'quotient_action_kernel': '16.14', 'quotient_action_kernel_order': 16, 'quotient_fusion': None, 'short_label': '96.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514919
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.a1.a1', '8.a1.a1', '8.a1.b1', '8.b1.a1', '8.c1.a1'], 'core': '2.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3850, 3292, 2974, 4167, 2302, 3876, 6682, 3762], 'generators': [2, 48, 192, 4, 24, 384, 96, 36], 'label': '768.1088652.2.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68514920
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.b1'], 'contains': ['24.j1.a1', '24.k1.a1', '24.l1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2239, -1, 7440, -1, 7325, -1, 6299, -1], 'generators': [1, 648], 'label': '768.1088652.12.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514921
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '48.f1.a1', '48.g1.a1', '48.i1.a1', '48.o1.a1'], 'contains': ['192.b1.a1', '192.c1.a1', '192.f1.a1', '192.g1.b1', '192.l1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2347, -1, 8226, -1, 7911, -1, 6807, -1], 'generators': [2, 12, 480], 'label': '768.1088652.96.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514922
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.b1', '48.d1.b1', '48.e1.b1', '48.f1.b1', '48.g1.a1', '48.i1.b1', '48.o1.b1'], 'contains': ['192.b1.a1', '192.c1.b1', '192.f1.b1', '192.g1.a1', '192.l1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2347, -1, 7053, -1, 7911, -1, 5921, -1], 'generators': [2, 636, 480], 'label': '768.1088652.96.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514923
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.i1.a1', '48.o1.a1'], 'contains': ['192.b1.a1', '192.c1.a1', '192.f2.a1', '192.g2.b1', '192.l2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2925, -1, 6180, -1, 7308, -1, 6593, -1], 'generators': [2, 12, 384], 'label': '768.1088652.96.b2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '96.b2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514924
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.b2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.i1.b1', '48.o1.b1'], 'contains': ['192.b1.a1', '192.c1.b1', '192.f2.b1', '192.g2.a1', '192.l2.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2925, -1, 5941, -1, 7308, -1, 5707, -1], 'generators': [2, 636, 384], 'label': '768.1088652.96.b2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '96.b2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.b2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514925
{'ambient': '768.1088652', 'aut_centralizer_order': 512, 'aut_label': '96.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.j1.a1', '48.k1.a1', '48.l1.a1', '48.m1.a1', '48.n1.a1', '48.p1.a1'], 'contains': ['192.b1.a1', '192.h1.a1', '192.i1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5288, -1, 4630, -1, 6209, -1, 2375, -1], 'generators': [2, 624], 'label': '768.1088652.96.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.c1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514928
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.c1.a1', '48.c1.b1', '48.e1.a1', '48.e1.b1', '48.k1.a1', '48.m1.a1', '48.r1.a1'], 'contains': ['192.b1.a1', '192.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3376, -1, 7603, -1, 8687, -1, 5814, -1], 'generators': [385, 480], 'label': '768.1088652.96.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514929
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.a1', '48.s1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [674, -1, 9734, -1, 9048, -1, 9050, -1], 'generators': [1, 12], 'label': '768.1088652.96.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514930
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.g1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.d1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.d1.b1', '48.s1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.d1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [674, -1, 8870, -1, 9048, -1, 8247, -1], 'generators': [1, 252], 'label': '768.1088652.96.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.g1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514931
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.b1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.d1.a1'], 'contains': ['24.j1.b1', '24.k1.b1', '24.l1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2239, -1, 6952, -1, 7325, -1, 5963, -1], 'generators': [1, 456], 'label': '768.1088652.12.b1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.b1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514932
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.s1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.p1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1119, -1, 9637, -1, 9263, -1, 8917, -1], 'generators': [25, 12], 'label': '768.1088652.96.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.a1', 'old_label': '96.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514933
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.h1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.s1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.p1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1119, -1, 8363, -1, 9263, -1, 7442, -1], 'generators': [217, 252], 'label': '768.1088652.96.h1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.e1.b1', 'old_label': '96.h1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.h1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514934
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.a1', '48.i1.a1'], 'contains': ['192.c1.a1', '192.n1.a1', '192.o1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [864, -1, 9494, -1, 7782, -1, 9158, -1], 'generators': [2, 492, 24], 'label': '768.1088652.96.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '96.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68514935
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b1.b1', '48.i1.b1'], 'contains': ['192.c1.b1', '192.n1.b1', '192.o1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [864, -1, 7230, -1, 7782, -1, 7683, -1], 'generators': [2, 636, 600], 'label': '768.1088652.96.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '96.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68514936
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.a1', '48.i1.a1', '48.s1.a1'], 'contains': ['192.c1.a1', '192.n2.a1', '192.o2.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [970, -1, 9839, -1, 8171, -1, 9239, -1], 'generators': [2, 12, 24], 'label': '768.1088652.96.i2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '96.i2.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514937
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.a2', '48.i1.a1', '48.s1.a2'], 'contains': ['192.c1.a1', '192.n2.a2', '192.o2.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [970, -1, 9558, -1, 8171, -1, 9320, -1], 'generators': [2, 396, 24], 'label': '768.1088652.96.i2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '96.i2.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514938
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.b1', '48.i1.b1', '48.s1.b1'], 'contains': ['192.c1.b1', '192.n2.b1', '192.o2.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [970, -1, 8285, -1, 8171, -1, 7764, -1], 'generators': [2, 348, 600], 'label': '768.1088652.96.i2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '96.i2.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514939
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.i2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.b2.b2', '48.i1.b1', '48.s1.b2'], 'contains': ['192.c1.b1', '192.n2.b2', '192.o2.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [970, -1, 8442, -1, 8171, -1, 7845, -1], 'generators': [2, 732, 600], 'label': '768.1088652.96.i2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '96.i2.b2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.i2.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514940
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.t1.a1', '48.u1.a1', '48.w1.a1'], 'contains': ['192.e1.a1', '192.f1.a1', '192.g1.b1', '192.l2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3031, -1, 7112, -1, 6799, -1, 6350, -1], 'generators': [386, 12, 480], 'label': '768.1088652.96.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '96.j1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514941
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.t1.b1', '48.u1.a1', '48.w1.b1'], 'contains': ['192.e1.a1', '192.f1.b1', '192.g1.a1', '192.l2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3031, -1, 6025, -1, 6799, -1, 5545, -1], 'generators': [386, 636, 480], 'label': '768.1088652.96.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '96.j1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514942
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.c1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.i1.a1', '24.i1.b1', '24.j1.a1', '24.j1.b1', '24.n1.a1', '24.o1.a1', '24.r1.a1', '24.t1.a1', '24.t1.b1', '24.u1.a1', '24.u1.b1', '24.bc1.a1', '24.be1.a1', '24.bi1.a1', '24.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6987, -1, 2512, -1, 1246, -1, 2226, -1], 'generators': [2, 12, 648, 576], 'label': '768.1088652.12.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.c1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68514943
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.j2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.v1.a1', '48.w1.a1'], 'contains': ['192.e1.a1', '192.f2.a1', '192.g2.b1', '192.l1.a1', '192.l2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3138, -1, 6268, -1, 6609, -1, 6512, -1], 'generators': [482, 12, 384], 'label': '768.1088652.96.j2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '96.j2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514944
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.j2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.v1.a1', '48.w1.b1'], 'contains': ['192.e1.a1', '192.f2.b1', '192.g2.a1', '192.l1.b1', '192.l2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3138, -1, 5779, -1, 6609, -1, 5626, -1], 'generators': [482, 636, 384], 'label': '768.1088652.96.j2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '96.j2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.j2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514945
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.u1.a1', '48.x1.a1', '48.y1.a1'], 'contains': ['192.e1.a1', '192.h1.a1', '192.i1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7084, -1, 4406, -1, 5296, -1, 1041, -1], 'generators': [386, 624], 'label': '768.1088652.96.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '96.k1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.k1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514946
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.v1.a1', '48.x1.a1'], 'contains': ['192.e1.a1', '192.j1.a1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7260, -1, 4159, -1, 4379, -1, 2509, -1], 'generators': [482, 648], 'label': '768.1088652.96.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '96.l1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.l1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514947
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.u1.a1', '48.z1.a1'], 'contains': ['192.f1.a1', '192.g1.a1', '192.i1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3597, -1, 5711, -1, 6045, -1, 4635, -1], 'generators': [626, 12], 'label': '768.1088652.96.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.m1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514948
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.u1.a1', '48.z1.b1'], 'contains': ['192.f1.b1', '192.g1.b1', '192.i1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3597, -1, 5397, -1, 6045, -1, 4870, -1], 'generators': [626, 636], 'label': '768.1088652.96.m1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.m1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.m1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514949
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.v1.a1', '48.ba1.a1'], 'contains': ['192.f2.a1', '192.g2.a1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5043, -1, 4922, -1, 5460, -1, 5042, -1], 'generators': [602, 12], 'label': '768.1088652.96.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.n1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514950
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.v1.a1', '48.ba1.b1'], 'contains': ['192.f2.b1', '192.g2.b1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5043, -1, 5003, -1, 5460, -1, 5184, -1], 'generators': [26, 636], 'label': '768.1088652.96.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.n1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.n1.b1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514951
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.w1.a1', '48.bb1.a1'], 'contains': ['192.f1.a1', '192.g2.b1', '192.n1.a1', '192.n2.a1', '192.n2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2118, -1, 8586, -1, 7437, -1, 8140, -1], 'generators': [26, 12, 480], 'label': '768.1088652.96.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.o1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514952
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.o1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.w1.b1', '48.bb1.b1'], 'contains': ['192.f1.b1', '192.g2.a1', '192.n1.b1', '192.n2.b1', '192.n2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2118, -1, 6897, -1, 7437, -1, 6431, -1], 'generators': [602, 636, 480], 'label': '768.1088652.96.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.o1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514953
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.d1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.d1.a1', '6.d1.b1'], 'contains': ['24.c1.a1', '24.d1.a1', '24.k1.a1', '24.k1.b1', '24.m1.a1', '24.p1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2870, -1, 7075, -1, 7595, -1, 6131, -1], 'generators': [1, 12, 624, 384], 'label': '768.1088652.12.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.d1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514954
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.o2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.w1.a1', '48.bb1.a1'], 'contains': ['192.f2.a1', '192.g1.b1', '192.g2.b1', '192.n1.a1', '192.n2.a1', '192.n2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2241, -1, 8527, -1, 7178, -1, 8059, -1], 'generators': [26, 12, 384], 'label': '768.1088652.96.o2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '96.o2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514955
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.o2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.w1.b1', '48.bb1.b1'], 'contains': ['192.f2.b1', '192.g1.a1', '192.g2.a1', '192.n1.b1', '192.n2.b1', '192.n2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2241, -1, 6602, -1, 7178, -1, 6270, -1], 'generators': [602, 636, 384], 'label': '768.1088652.96.o2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '96.o2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.o2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514956
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.p1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.u1.a1', '48.bg1.a1'], 'contains': ['192.f1.a1', '192.f1.b1', '192.h1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3913, -1, 5241, -1, 5688, -1, 4951, -1], 'generators': [12, 624], 'label': '768.1088652.96.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.p1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.p1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514957
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.q1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.v1.a1', '48.bh1.a1'], 'contains': ['192.f2.a1', '192.f2.b1', '192.j1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5485, -1, 5072, -1, 4802, -1, 5255, -1], 'generators': [12, 600], 'label': '768.1088652.96.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.q1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.q1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514958
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.i1.a1', '48.w1.a1'], 'contains': ['192.f1.a1', '192.f2.a1', '192.o1.a1', '192.o2.a1', '192.o2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2012, -1, 8645, -1, 7048, -1, 8516, -1], 'generators': [12, 24, 480], 'label': '768.1088652.96.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.r1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514959
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.r1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.i1.b1', '48.w1.b1'], 'contains': ['192.f1.b1', '192.f2.b1', '192.o1.b1', '192.o2.b1', '192.o2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2012, -1, 6543, -1, 7048, -1, 7130, -1], 'generators': [636, 600, 480], 'label': '768.1088652.96.r1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.r1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.r1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514960
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.t1.b1', '48.bl1.a1'], 'contains': ['192.g1.a1', '192.p1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2488, -1, 6975, -1, 7609, -1, 5438, -1], 'generators': [601, 480], 'label': '768.1088652.96.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.l1.b1', 'old_label': '96.s1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514961
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.s1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.t1.a1', '48.bl1.b1'], 'contains': ['192.g1.b1', '192.p1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2488, -1, 8149, -1, 7609, -1, 7237, -1], 'generators': [25, 480], 'label': '768.1088652.96.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.l1.a1', 'old_label': '96.s1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.s1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514962
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '48.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.g1.a1', '48.u1.a1', '48.bm1.a1'], 'contains': ['192.g1.a1', '192.g1.b1', '192.h1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [4158, -1, 5546, -1, 5801, -1, 4717, -1], 'generators': [14, 624], 'label': '768.1088652.96.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '96.t1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.t1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514963
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.u1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.h1.a1', '48.v1.a1', '48.bn1.a1'], 'contains': ['192.g2.a1', '192.g2.b1', '192.j1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [5681, -1, 4839, -1, 4916, -1, 5113, -1], 'generators': [638, 648], 'label': '768.1088652.96.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.n1.a1', 'old_label': '96.u1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.u1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514964
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.a1', '6.e1.b1'], 'contains': ['24.l1.b1', '24.m1.a1', '24.v1.a1', '24.bj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3120, -1, 6492, -1, 7063, -1, 5614, -1], 'generators': [601, 12, 624], 'label': '768.1088652.12.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514965
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.x1.a1', '48.bp1.a1'], 'contains': ['192.h1.a1', '192.j1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7626, -1, 3562, -1, 3772, -1, 1311, -1], 'generators': [300, 624], 'label': '768.1088652.96.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.v1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.v1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514966
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.x1.a1', '48.bq1.a1'], 'contains': ['192.h1.a1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [8151, -1, 3614, -1, 4000, -1, 1143, -1], 'generators': [302, 624], 'label': '768.1088652.96.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '96.w1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.w1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514967
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.x1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.j1.a1', '48.x1.a1', '48.br1.a1'], 'contains': ['192.i1.a1', '192.j1.a1', '192.k1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [8248, -1, 3665, -1, 3886, -1, 1231, -1], 'generators': [578, 648], 'label': '768.1088652.96.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.o1.a1', 'old_label': '96.x1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.x1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514968
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.y1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.n1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.n1.a1', '48.y1.a1', '48.bs1.a1'], 'contains': ['192.i1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [9682, -1, 4481, -1, 5574, -1, 360, -1], 'generators': [577], 'label': '768.1088652.96.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.q1.a1', 'old_label': '96.y1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.y1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514969
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.a1', '48.o1.a1', '48.z1.a1', '48.ba1.a1', '48.bb1.a1', '48.bc1.a1', '48.bd1.a1', '48.be1.a1', '48.bf1.a1', '48.bg1.a1', '48.bh1.a1'], 'contains': ['192.a1.a1', '192.f1.a1', '192.f2.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4394, -1, 3935, -1, 4551, -1, 4064, -1], 'generators': [12, 480, 384], 'label': '768.1088652.96.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.z1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514970
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.a1.b1', '48.o1.b1', '48.z1.b1', '48.ba1.b1', '48.bb1.b1', '48.bc1.b1', '48.bd1.b1', '48.be1.b1', '48.bf1.b1', '48.bg1.a1', '48.bh1.a1'], 'contains': ['192.a1.a1', '192.f1.b1', '192.f2.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4394, -1, 3720, -1, 4551, -1, 4179, -1], 'generators': [636, 480, 384], 'label': '768.1088652.96.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.z1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.z1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514971
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.b1', '48.z1.a1', '48.ba1.a1', '48.bb1.b1', '48.bi1.a1', '48.bj1.a1', '48.bk1.a1', '48.bl1.a1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.a1.a1', '192.g1.a1', '192.g2.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4540, -1, 3994, -1, 4681, -1, 3808, -1], 'generators': [638, 480, 384], 'label': '768.1088652.96.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.ba1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514972
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.ba1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.o1.a1', '48.z1.b1', '48.ba1.b1', '48.bb1.a1', '48.bi1.b1', '48.bj1.b1', '48.bk1.b1', '48.bl1.b1', '48.bm1.a1', '48.bn1.a1'], 'contains': ['192.a1.a1', '192.g1.b1', '192.g2.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4540, -1, 3779, -1, 4681, -1, 3969, -1], 'generators': [14, 480, 384], 'label': '768.1088652.96.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.ba1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514973
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.b1.a1', '48.p1.a1', '48.bc1.a1', '48.bc1.b1', '48.bg1.a1', '48.bi1.a1', '48.bi1.b1', '48.bm1.a1', '48.bo1.a1', '48.bp1.a1', '48.bq1.a1'], 'contains': ['192.a1.a1', '192.h1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6285, -1, 2284, -1, 2416, -1, 2072, -1], 'generators': [624, 384], 'label': '768.1088652.96.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bb1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514974
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '96.bc1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.p1.a1', '48.z1.a1', '48.z1.b1', '48.bd1.a1', '48.bd1.b1', '48.bj1.a1', '48.bj1.b1', '48.bo1.a1', '48.br1.a1', '48.bs1.a1'], 'contains': ['192.a1.a1', '192.i1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7491, -1, 3857, -1, 4164, -1, 1794, -1], 'generators': [626, 384], 'label': '768.1088652.96.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '96.bc1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '8.3'}
-
id: 68514975
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.e1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1', '6.d1.b1', '6.e1.a1'], 'contains': ['24.l1.a1', '24.m1.a1', '24.v1.b1', '24.bj1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3120, -1, 6834, -1, 7063, -1, 5799, -1], 'generators': [25, 12, 624], 'label': '768.1088652.12.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.e1.b1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514976
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.bd1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.bc1.a1', '48.bc1.b1', '48.be1.a1', '48.be1.b1', '48.bh1.a1', '48.bj1.a1', '48.bj1.b1', '48.bk1.a1', '48.bk1.b1', '48.bn1.a1', '48.bp1.a1', '48.br1.a1', '48.bt1.a1', '48.bu1.a1'], 'contains': ['192.a1.a1', '192.j1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6628, -1, 2120, -1, 1986, -1, 2777, -1], 'generators': [648, 480], 'label': '768.1088652.96.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.bd1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514977
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '96.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '8.3', 'aut_weyl_index': 768, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.q1.a1', '48.ba1.a1', '48.ba1.b1', '48.bd1.a1', '48.bd1.b1', '48.bf1.a1', '48.bf1.b1', '48.bi1.a1', '48.bi1.b1', '48.bk1.a1', '48.bk1.b1', '48.bq1.a1', '48.br1.a1', '48.bt1.a1'], 'contains': ['192.a1.a1', '192.k1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6908, -1, 2644, -1, 2201, -1, 2241, -1], 'generators': [650, 480], 'label': '768.1088652.96.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '96.be1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.be1.a1', 'subgroup_fusion': None, 'weyl_group': '4.2'}
-
id: 68514978
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.a1', '48.bv1.a1', '48.bv1.a2'], 'contains': ['192.l1.a1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1871, -1, 9115, -1, 9693, -1, 7576, -1], 'generators': [385, 12], 'label': '768.1088652.96.bf1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '96.bf1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514979
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.bf1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.e1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.e1.b1', '48.bv1.b1', '48.bv1.b2'], 'contains': ['192.l1.b1', '192.m1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1871, -1, 7899, -1, 9693, -1, 6162, -1], 'generators': [385, 252], 'label': '768.1088652.96.bf1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '96.bf1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bf1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514980
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.a1', '48.bv1.a1', '48.bv1.a2'], 'contains': ['192.l1.a1', '192.p1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1608, -1, 9271, -1, 9478, -1, 7952, -1], 'generators': [409, 12], 'label': '768.1088652.96.bg1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.a1', 'old_label': '96.bg1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514981
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '96.bg1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '4.2', 'aut_weyl_index': 1536, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.f1.b1', '48.bv1.b1', '48.bv1.b2'], 'contains': ['192.l1.b1', '192.p1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1608, -1, 7996, -1, 9478, -1, 6028, -1], 'generators': [601, 252], 'label': '768.1088652.96.bg1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.f1.b1', 'old_label': '96.bg1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bg1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514982
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.w1.a1'], 'contains': ['192.l1.a1', '192.l2.a1', '192.n1.a1', '192.n2.a1', '192.n2.a2', '192.o1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1308, -1, 9193, -1, 8041, -1, 8435, -1], 'generators': [482, 492, 24], 'label': '768.1088652.96.bh1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '96.bh1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514983
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.w1.b1'], 'contains': ['192.l1.b1', '192.l2.b1', '192.n1.b1', '192.n2.b1', '192.n2.b2', '192.o1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1308, -1, 7171, -1, 8041, -1, 6969, -1], 'generators': [482, 636, 600], 'label': '768.1088652.96.bh1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '96.bh1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514984
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.w1.a1', '48.bv1.a1'], 'contains': ['192.l1.a1', '192.l2.a1', '192.n1.a1', '192.n2.a2', '192.o2.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1414, -1, 9376, -1, 8300, -1, 8355, -1], 'generators': [482, 12, 24], 'label': '768.1088652.96.bh2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.bh2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514985
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.a1', '48.w1.a1', '48.bv1.a2'], 'contains': ['192.l1.a1', '192.l2.a1', '192.n1.a1', '192.n2.a1', '192.o2.a2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1414, -1, 9435, -1, 8300, -1, 8597, -1], 'generators': [482, 396, 24], 'label': '768.1088652.96.bh2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '96.bh2.a2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514986
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.f1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.26531', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1', '6.e1.a1', '6.e1.b1'], 'contains': ['24.m1.a1', '24.q1.a1', '24.w1.a1', '24.w1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6193, -1, 5865, -1, 5923, -1, 2051, -1], 'generators': [577, 12, 624], 'label': '768.1088652.12.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.f1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68514987
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.w1.b1', '48.bv1.b1'], 'contains': ['192.l1.b1', '192.l2.b1', '192.n1.b1', '192.n2.b1', '192.o2.b2'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1414, -1, 7289, -1, 8300, -1, 6888, -1], 'generators': [482, 732, 600], 'label': '768.1088652.96.bh2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.bh2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514988
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '96.bh2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['48.i1.b1', '48.w1.b1', '48.bv1.b2'], 'contains': ['192.l1.b1', '192.l2.b1', '192.n1.b1', '192.n2.b2', '192.o2.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1414, -1, 7348, -1, 8300, -1, 7049, -1], 'generators': [482, 348, 600], 'label': '768.1088652.96.bh2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '96.bh2.b2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '96.bh2.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514989
{'ambient': '768.1088652', 'aut_centralizer_order': 48, 'aut_label': '128.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '32.b1.a1', '32.b1.b1', '32.b2.a1', '32.b2.a2', '32.b2.b1', '32.b2.b2', '64.a1.a1'], 'contains': ['256.a1.a1', '384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [343, -1, 8908, -1, 7142, -1, 9472, -1], 'generators': [2, 4], 'label': '768.1088652.128.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '2.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '128.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '128.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514990
{'ambient': '768.1088652', 'aut_centralizer_order': 1024, 'aut_label': '192.a1', 'aut_quo_index': 3, 'aut_stab_index': 1, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '6.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '96.a1.a1', '96.z1.a1', '96.z1.b1', '96.ba1.a1', '96.ba1.b1', '96.bb1.a1', '96.bc1.a1', '96.bd1.a1', '96.be1.a1'], 'contains': ['384.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4786, 4300, 3888, 4731, 4164, 5328, 3969, 5059], 'generators': [480, 384], 'label': '768.1088652.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['48.a1.a1', '48.a1.b1', '48.b1.a1', '96.a1.a1'], 'normal_contains': ['768.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': '6.1', 'quotient_action_kernel': '32.51', 'quotient_action_kernel_order': 32, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68514991
{'ambient': '768.1088652', 'aut_centralizer_order': 2048, 'aut_label': '192.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.b1.a1', '96.b1.b1', '96.b2.a1', '96.b2.b1', '96.c1.a1', '96.d1.a1', '96.e1.a1', '96.f1.a1'], 'contains': ['384.a1.a1', '384.b1.a1', '384.c1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3872, -1, 5713, -1, 7020, -1, 5895, -1], 'generators': [2, 480], 'label': '768.1088652.192.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '192.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514992
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.b2.a1', '96.g1.a1', '96.h1.a1', '96.i1.a1', '96.i2.a1', '96.i2.a2'], 'contains': ['384.a1.a1', '384.d1.a1', '384.e1.b1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1324, -1, 9421, -1, 7911, -1, 8313, -1], 'generators': [2, 12], 'label': '768.1088652.192.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514993
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.c1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.b2.b1', '96.g1.b1', '96.h1.b1', '96.i1.b1', '96.i2.b1', '96.i2.b2'], 'contains': ['384.a1.a1', '384.d1.b1', '384.e1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1324, -1, 8210, -1, 7911, -1, 7439, -1], 'generators': [2, 636], 'label': '768.1088652.192.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.c1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.c1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514994
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.d1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.e1.a1', '96.g1.a1', '96.g1.b1'], 'contains': ['384.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [656, -1, 9476, -1, 8472, -1, 8389, -1], 'generators': [1], 'label': '768.1088652.192.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.d1.a1', 'old_label': '192.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68514995
{'ambient': '768.1088652', 'aut_centralizer_order': 1024, 'aut_label': '192.e1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '6.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.a1.a1', '96.j1.a1', '96.j1.b1', '96.j2.a1', '96.j2.b1', '96.k1.a1', '96.l1.a1'], 'contains': ['384.b1.a1', '384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4016, -1, 5445, -1, 6372, -1, 5545, -1], 'generators': [386, 480], 'label': '768.1088652.192.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '192.e1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.e1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514996
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.j1.a1', '96.m1.a1', '96.o1.a1', '96.p1.a1', '96.r1.a1', '96.z1.a1'], 'contains': ['384.b1.a1', '384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2936, -1, 6450, -1, 6761, -1, 6423, -1], 'generators': [12, 480], 'label': '768.1088652.192.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '192.f1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514997
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '12.g1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.b1.a1', '6.c1.a1'], 'contains': ['24.b1.a1', '24.i1.a1', '24.i1.b1', '24.m1.a1', '24.o1.a1', '24.s1.a1', '24.s1.b1', '24.bb1.a1', '24.bd1.a1', '24.bh1.a1', '24.bk1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [7483, -1, 3562, -1, 2457, -1, 1359, -1], 'generators': [2, 12, 624, 576], 'label': '768.1088652.12.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.g1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68514998
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.f1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.j1.b1', '96.m1.b1', '96.o1.b1', '96.p1.a1', '96.r1.b1', '96.z1.b1'], 'contains': ['384.b1.a1', '384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2936, -1, 5504, -1, 6761, -1, 5707, -1], 'generators': [636, 480], 'label': '768.1088652.192.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '192.f1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68514999
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.f2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.j2.a1', '96.n1.a1', '96.o2.a1', '96.q1.a1', '96.r1.a1', '96.z1.a1'], 'contains': ['384.b1.a1', '384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3620, -1, 6173, -1, 6502, -1, 6504, -1], 'generators': [12, 384], 'label': '768.1088652.192.f2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '192.f2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515000
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.f2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.j2.b1', '96.n1.b1', '96.o2.b1', '96.q1.a1', '96.r1.b1', '96.z1.b1'], 'contains': ['384.b1.a1', '384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3620, -1, 5166, -1, 6502, -1, 5787, -1], 'generators': [636, 384], 'label': '768.1088652.192.f2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '192.f2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.f2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515001
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.j1.b1', '96.m1.a1', '96.o2.b1', '96.s1.a1', '96.t1.a1', '96.ba1.a1'], 'contains': ['384.b1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3231, -1, 5574, -1, 6890, -1, 5464, -1], 'generators': [638, 480], 'label': '768.1088652.192.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '192.g1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515002
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.j1.a1', '96.m1.b1', '96.o2.a1', '96.s1.b1', '96.t1.a1', '96.ba1.b1'], 'contains': ['384.b1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3231, -1, 6391, -1, 6890, -1, 6262, -1], 'generators': [14, 480], 'label': '768.1088652.192.g1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '192.g1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g1.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515003
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.g2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.j2.b1', '96.n1.a1', '96.o1.b1', '96.o2.b1', '96.u1.a1', '96.ba1.a1'], 'contains': ['384.b1.a1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3726, -1, 5084, -1, 6631, -1, 5626, -1], 'generators': [638, 384], 'label': '768.1088652.192.g2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.a1', 'old_label': '192.g2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515004
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.g2', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.j2.a1', '96.n1.b1', '96.o1.a1', '96.o2.a1', '96.u1.a1', '96.ba1.b1'], 'contains': ['384.b1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [3726, -1, 5846, -1, 6631, -1, 6342, -1], 'generators': [14, 384], 'label': '768.1088652.192.g2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.i1.b1', 'old_label': '192.g2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.g2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515005
{'ambient': '768.1088652', 'aut_centralizer_order': 512, 'aut_label': '192.h1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.k1.a1', '96.p1.a1', '96.t1.a1', '96.v1.a1', '96.w1.a1', '96.bb1.a1'], 'contains': ['384.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5894, -1, 4376, -1, 5378, -1, 2234, -1], 'generators': [624], 'label': '768.1088652.192.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '192.h1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.h1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515006
{'ambient': '768.1088652', 'aut_centralizer_order': 512, 'aut_label': '192.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '12.k1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.c1.a1', '96.k1.a1', '96.m1.a1', '96.m1.b1', '96.x1.a1', '96.y1.a1', '96.bc1.a1'], 'contains': ['384.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7539, -1, 4512, -1, 5574, -1, 2076, -1], 'generators': [626], 'label': '768.1088652.192.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.b1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '192.i1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.i1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515007
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.j1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.l1.a1', '96.q1.a1', '96.u1.a1', '96.v1.a1', '96.x1.a1', '96.bd1.a1'], 'contains': ['384.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [6913, -1, 4071, -1, 4379, -1, 2710, -1], 'generators': [648], 'label': '768.1088652.192.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.j1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.j1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515008
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '6.d1.b1'], 'contains': ['24.a1.a1', '24.e1.a1', '24.f1.a1', '24.k1.a1', '24.l1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1297, -1, 8411, -1, 7902, -1, 7380, -1], 'generators': [1, 24, 384], 'label': '768.1088652.12.h1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '12.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515009
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.d1.a1', '96.l1.a1', '96.n1.a1', '96.n1.b1', '96.w1.a1', '96.x1.a1', '96.be1.a1'], 'contains': ['384.b1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [7147, -1, 4197, -1, 4493, -1, 2541, -1], 'generators': [650], 'label': '768.1088652.192.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.c1.a1', 'old_label': '192.k1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.k1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515010
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '96.j2.a1', '96.bf1.a1', '96.bg1.a1', '96.bh1.a1', '96.bh2.a1', '96.bh2.a2'], 'contains': ['384.c1.a1', '384.d1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1859, -1, 8948, -1, 8041, -1, 7857, -1], 'generators': [482, 12], 'label': '768.1088652.192.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.l1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515011
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '192.l1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b1.b1', '96.j2.b1', '96.bf1.b1', '96.bg1.b1', '96.bh1.b1', '96.bh2.b1', '96.bh2.b2'], 'contains': ['384.c1.a1', '384.d1.b1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1859, -1, 7694, -1, 8041, -1, 6736, -1], 'generators': [482, 636], 'label': '768.1088652.192.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.l1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515012
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.l2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.a1', '96.j1.a1', '96.j2.a1', '96.bh1.a1', '96.bh2.a1', '96.bh2.a2'], 'contains': ['384.c1.a1', '384.d1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2080, -1, 8757, -1, 7523, -1, 7520, -1], 'generators': [386, 12], 'label': '768.1088652.192.l2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '192.l2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l2.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515013
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.l2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.b2.b1', '96.j1.b1', '96.j2.b1', '96.bh1.b1', '96.bh2.b1', '96.bh2.b2'], 'contains': ['384.c1.a1', '384.d1.b1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2080, -1, 6333, -1, 7523, -1, 6656, -1], 'generators': [386, 636], 'label': '768.1088652.192.l2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '192.l2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.l2.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515014
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '192.m1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.f1.a1', '96.bf1.a1', '96.bf1.b1'], 'contains': ['384.c1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [2301, -1, 8391, -1, 8700, -1, 6812, -1], 'generators': [385], 'label': '768.1088652.192.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.c1.a1', 'old_label': '192.m1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.m1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515015
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.a1', '96.o1.a1', '96.o2.a1', '96.bh1.a1', '96.bh2.a1', '96.bh2.a2'], 'contains': ['384.d1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1617, -1, 9193, -1, 7652, -1, 8152, -1], 'generators': [410, 12], 'label': '768.1088652.192.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.a1', 'old_label': '192.n1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515016
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n1', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i1.b1', '96.o1.b1', '96.o2.b1', '96.bh1.b1', '96.bh2.b1', '96.bh2.b2'], 'contains': ['384.d1.b1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 24, 'diagramx': [1617, -1, 7205, -1, 7652, -1, 6969, -1], 'generators': [602, 636], 'label': '768.1088652.192.n1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '24.a1.b1', 'old_label': '192.n1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515017
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.a1', '96.o1.a1', '96.o2.a1', '96.bh1.a1', '96.bh2.a2'], 'contains': ['384.d1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1511, -1, 9076, -1, 7782, -1, 8232, -1], 'generators': [26, 12], 'label': '768.1088652.192.n2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.n2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515018
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.a2', '96.o1.a1', '96.o2.a1', '96.bh1.a1', '96.bh2.a1'], 'contains': ['384.d1.a1', '384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1511, -1, 9134, -1, 7782, -1, 8071, -1], 'generators': [506, 12], 'label': '768.1088652.192.n2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '192.n2.a2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n2.a2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515019
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.b1', '6.d1.a1'], 'contains': ['24.a1.b1', '24.e1.b1', '24.f1.b1', '24.k1.b1', '24.l1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [1297, -1, 7348, -1, 7902, -1, 6929, -1], 'generators': [1, 600, 384], 'label': '768.1088652.12.h1.b1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '12.h1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.h1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515020
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.b1', '96.o1.b1', '96.o2.b1', '96.bh1.b1', '96.bh2.b1'], 'contains': ['384.d1.b1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1511, -1, 7324, -1, 7782, -1, 6888, -1], 'generators': [698, 636], 'label': '768.1088652.192.n2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.n2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n2.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515021
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.n2', 'aut_quo_index': None, 'aut_stab_index': 48, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.i2.b2', '96.o1.b1', '96.o2.b1', '96.bh1.b1', '96.bh2.b2'], 'contains': ['384.d1.b1', '384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1511, -1, 7265, -1, 7782, -1, 7049, -1], 'generators': [218, 636], 'label': '768.1088652.192.n2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '192.n2.b2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.n2.b2', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515022
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.a1', '96.i1.a1', '96.r1.a1', '96.bh1.a1'], 'contains': ['384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1112, -1, 8839, -1, 7263, -1, 8465, -1], 'generators': [492, 24], 'label': '768.1088652.192.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.a1', 'old_label': '192.o1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68515023
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c1.b1', '96.i1.b1', '96.r1.b1', '96.bh1.b1'], 'contains': ['384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [1112, -1, 6714, -1, 7263, -1, 7601, -1], 'generators': [636, 600], 'label': '768.1088652.192.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.a1.b1', 'old_label': '192.o1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o1.b1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
id: 68515024
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.a1', '96.i2.a1', '96.r1.a1', '96.bh2.a1'], 'contains': ['384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1218, -1, 9303, -1, 7393, -1, 8546, -1], 'generators': [12, 24], 'label': '768.1088652.192.o2.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '192.o2.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o2.a1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68515025
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.a2', '96.i2.a2', '96.r1.a1', '96.bh2.a2'], 'contains': ['384.d1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1218, -1, 9362, -1, 7393, -1, 8626, -1], 'generators': [396, 24], 'label': '768.1088652.192.o2.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '192.o2.a2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o2.a2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68515026
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.b1', '96.i2.b1', '96.r1.b1', '96.bh2.b2'], 'contains': ['384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1218, -1, 6772, -1, 7393, -1, 7682, -1], 'generators': [348, 600], 'label': '768.1088652.192.o2.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '192.o2.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o2.b1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68515027
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '192.o2', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '6.1', 'aut_weyl_index': 1024, 'centralizer': '24.a1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.c2.b2', '96.i2.b2', '96.r1.b1', '96.bh2.b1'], 'contains': ['384.d1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1218, -1, 6926, -1, 7393, -1, 7762, -1], 'generators': [732, 600], 'label': '768.1088652.192.o2.b2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '192.o2.b2', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.o2.b2', 'subgroup_fusion': None, 'weyl_group': '6.1'}
-
id: 68515028
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.b1', '96.s1.a1', '96.bg1.b1'], 'contains': ['384.e1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1738, -1, 7903, -1, 8586, -1, 6580, -1], 'generators': [601], 'label': '768.1088652.192.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.f1.b1', 'old_label': '192.p1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515029
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '192.p1', 'aut_quo_index': None, 'aut_stab_index': 96, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '48.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['96.h1.a1', '96.s1.b1', '96.bg1.a1'], 'contains': ['384.e1.b1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 48, 'diagramx': [1738, -1, 9249, -1, 8586, -1, 7969, -1], 'generators': [25], 'label': '768.1088652.192.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '48.f1.a1', 'old_label': '192.p1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '192.p1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515030
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '3.a1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1024.diw', 'aut_weyl_index': 6, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.a1.a1', '6.b1.a1', '6.c1.a1', '6.d1.a1', '6.d1.b1', '6.e1.a1', '6.e1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4813, -1, 6206, -1, 5515, -1, 5021, -1], 'generators': [1, 24, 576], 'label': '768.1088652.3.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68515031
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.a1', '6.e1.a1'], 'contains': ['24.a1.b1', '24.i1.b1', '24.j1.b1', '24.m1.a1', '24.n1.a1', '24.x1.b1', '24.y1.b1', '24.z1.a1', '24.ba1.a1', '24.bf1.b1', '24.bg1.a1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [4762, -1, 4275, -1, 4660, -1, 4300, -1], 'generators': [2, 12, 600, 624], 'label': '768.1088652.12.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515032
{'ambient': '768.1088652', 'aut_centralizer_order': 48, 'aut_label': '256.a1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '2.1', 'aut_weyl_index': 3072, 'centralizer': '128.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['64.b1.a1', '64.c1.a1', '64.c1.b1', '64.c2.a1', '64.c2.a2', '64.c2.b1', '64.c2.b2', '128.a1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 64, 'diagramx': [512, -1, 7211, -1, 6277, -1, 8814, -1], 'generators': [4], 'label': '768.1088652.256.a1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '64.a1.a1', 'old_label': '256.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256.a1.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
-
id: 68515033
{'ambient': '768.1088652', 'aut_centralizer_order': 6144, 'aut_label': '384.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['128.a1.a1', '192.b1.a1', '192.c1.a1', '192.c1.b1', '192.d1.a1'], 'contains': ['768.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1318, 5631, 8569, 6152, 7761, 7155, 8227, 6611], 'generators': [2], 'label': '768.1088652.384.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '384.a1.a1', 'normal_contained_in': ['96.a1.a1'], 'normal_contains': ['768.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '384.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '1.1', 'quotient_action_kernel': '384.18135', 'quotient_action_kernel_order': 384, 'quotient_fusion': None, 'short_label': '384.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515034
{'ambient': '768.1088652', 'aut_centralizer_order': 2048, 'aut_label': '384.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '192.b1.a1', '192.e1.a1', '192.f1.a1', '192.f1.b1', '192.f2.a1', '192.f2.b1', '192.g1.a1', '192.g1.b1', '192.g2.a1', '192.g2.b1', '192.h1.a1', '192.i1.a1', '192.j1.a1', '192.k1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3963, -1, 5482, -1, 6446, -1, 5666, -1], 'generators': [480], 'label': '768.1088652.384.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '384.b1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.b1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515035
{'ambient': '768.1088652', 'aut_centralizer_order': 2048, 'aut_label': '384.c1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '3.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.b1.a1', '192.e1.a1', '192.l1.a1', '192.l1.b1', '192.l2.a1', '192.l2.b1', '192.m1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [2227, -1, 7461, -1, 7530, -1, 6810, -1], 'generators': [482], 'label': '768.1088652.384.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '96.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '384.c1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.c1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515036
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '192.f1.a1', '192.f2.a1', '192.l1.a1', '192.l2.a1', '192.n1.a1', '192.n2.a1', '192.n2.a2', '192.o1.a1', '192.o2.a1', '192.o2.a2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1638, -1, 8894, -1, 7417, -1, 8111, -1], 'generators': [12], 'label': '768.1088652.384.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '384.d1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515037
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '384.d1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.b1', '192.f1.b1', '192.f2.b1', '192.l1.b1', '192.l2.b1', '192.n1.b1', '192.n2.b1', '192.n2.b2', '192.o1.b1', '192.o2.b1', '192.o2.b2'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1638, -1, 6953, -1, 7417, -1, 7009, -1], 'generators': [636], 'label': '768.1088652.384.d1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '48.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '384.d1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.d1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515038
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.b1', '192.g1.a1', '192.g2.a1', '192.l1.b1', '192.l2.b1', '192.n1.b1', '192.n2.b1', '192.n2.b2', '192.p1.a1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1760, -1, 7304, -1, 7647, -1, 6738, -1], 'generators': [638], 'label': '768.1088652.384.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.b1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '384.e1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515057
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['32.b2.a2', '48.s1.a2', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [240, -1, 9302, -1, 9650, -1, 9366, -1], 'generators': [1, 408, 2, 4, 492], 'label': '768.1088652.16.b1.a2', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a2', 'old_label': '16.b1.a2', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a2', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515039
{'ambient': '768.1088652', 'aut_centralizer_order': 256, 'aut_label': '384.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '1.1', 'aut_weyl_index': 6144, 'centralizer': '12.h1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['192.c1.a1', '192.g1.b1', '192.g2.b1', '192.l1.a1', '192.l2.a1', '192.n1.a1', '192.n2.a1', '192.n2.a2', '192.p1.b1'], 'contains': ['768.a1.a1'], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [1760, -1, 9015, -1, 7647, -1, 7913, -1], 'generators': [14], 'label': '768.1088652.384.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '24.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '384.e1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '384.e1.b1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515040
{'ambient': '768.1088652', 'aut_centralizer_order': None, 'aut_label': '768.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['256.a1.a1', '384.a1.a1', '384.b1.a1', '384.c1.a1', '384.d1.a1', '384.d1.b1', '384.e1.a1', '384.e1.b1'], 'contains': [], 'core': '768.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1711, 4988, 7331, 5465, 7474, 6218, 7447, 5806], 'generators': [], 'label': '768.1088652.768.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '768.a1.a1', 'normal_contained_in': ['192.a1.a1', '384.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '768.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '768.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
-
id: 68515041
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '12.i1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1', '6.d1.b1', '6.e1.b1'], 'contains': ['24.a1.a1', '24.i1.a1', '24.j1.a1', '24.m1.a1', '24.n1.a1', '24.x1.a1', '24.y1.a1', '24.z1.b1', '24.ba1.b1', '24.bf1.a1', '24.bg1.b1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4762, -1, 4652, -1, 4660, -1, 4545, -1], 'generators': [2, 12, 24, 624], 'label': '768.1088652.12.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.i1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515042
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2194', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.b1.a1'], 'contains': ['24.g1.a1', '24.h1.a1', '24.o1.a1', '24.p1.a1', '24.q1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9538, -1, 5555, -1, 5634, -1, 407, -1], 'generators': [1, 588, 384], 'label': '768.1088652.12.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515043
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '12.k1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.261', 'aut_weyl_index': 96, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1.a1', '6.b1.a1'], 'contains': ['24.b1.a1', '24.p1.a1', '24.q1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7995, -1, 5428, -1, 5352, -1, 1189, -1], 'generators': [1, 576], 'label': '768.1088652.12.k1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '12.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515044
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1'], 'contains': ['24.v1.a1', '24.w1.a1', '24.y1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4503, -1, 6206, -1, 6193, -1, 3548, -1], 'generators': [577, 648], 'label': '768.1088652.12.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '12.l1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515045
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1'], 'contains': ['24.v1.b1', '24.w1.b1', '24.y1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4503, -1, 6096, -1, 6193, -1, 4102, -1], 'generators': [577, 456], 'label': '768.1088652.12.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '12.l1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.l1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515046
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.m1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.s1.a1', '24.s1.b1', '24.u1.a1', '24.u1.b1', '24.x1.a1', '24.x1.b1', '24.y1.a1', '24.y1.b1', '24.ba1.a1', '24.ba1.b1', '24.bc1.a1', '24.bh1.a1', '24.bi1.a1', '24.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6713, -1, 2676, -1, 1864, -1, 2572, -1], 'generators': [626, 12, 648, 576], 'label': '768.1088652.12.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '12.m1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.m1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515047
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.n1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '256.16888', 'aut_weyl_index': 24, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.t1.a1', '24.t1.b1', '24.x1.a1', '24.x1.b1', '24.z1.a1', '24.z1.b1', '24.bd1.a1', '24.bi1.a1', '24.bk1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5892, -1, 2378, -1, 1540, -1, 2976, -1], 'generators': [26, 12, 624, 576], 'label': '768.1088652.12.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.n1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.n1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515048
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.b1'], 'contains': ['24.v1.a1', '24.w1.a1', '24.bf1.a1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4296, -1, 6315, -1, 6435, -1, 3397, -1], 'generators': [577, 24], 'label': '768.1088652.12.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '12.o1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515049
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.o1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.e1.a1'], 'contains': ['24.v1.b1', '24.w1.b1', '24.bf1.b1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 6, 'diagramx': [4296, -1, 5987, -1, 6435, -1, 4785, -1], 'generators': [577, 600], 'label': '768.1088652.12.o1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '12.o1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.o1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515050
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '4.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['192.d1.a1', '192.m1.a1', '192.p1.b1', '192.p1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['12.a1.a1', '16.c1.a1', '16.c1.b1', '16.d1.a1', '16.e1.a1'], 'core': '4.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3815, 2191, 2663, 2990, 881, 1581, 6644, 1837], 'generators': [4, 96, 192, 36, 384, 24, 48], 'label': '768.1088652.4.a1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.a1.a1', 'projective_image': '768.1088652', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1.a1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
-
id: 68515051
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.s1.b1', '24.t1.b1', '24.u1.b1', '24.z1.b1', '24.ba1.b1', '24.bb1.a1', '24.be1.a1', '24.bf1.b1', '24.bg1.a1'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [6449, -1, 2900, -1, 2751, -1, 3724, -1], 'generators': [578, 12, 600, 624], 'label': '768.1088652.12.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515052
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '12.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.2163', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.a1.a1'], 'contains': ['24.s1.a1', '24.t1.a1', '24.u1.a1', '24.z1.a1', '24.ba1.a1', '24.bb1.a1', '24.be1.a1', '24.bf1.a1', '24.bg1.b1'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6449, -1, 3210, -1, 2751, -1, 2774, -1], 'generators': [578, 12, 24, 624], 'label': '768.1088652.12.p1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '12.p1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.p1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515053
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.bh1.a1', '24.bj1.a1', '24.bj1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5203, -1, 6612, -1, 4349, -1, 5309, -1], 'generators': [25, 588], 'label': '768.1088652.12.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.q1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.q1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515054
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '12.r1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '256.26539', 'aut_weyl_index': 24, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['6.c1.a1'], 'contains': ['24.bj1.a1', '24.bj1.b1', '24.bk1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5017, -1, 6715, -1, 4121, -1, 5451, -1], 'generators': [25, 576], 'label': '768.1088652.12.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.c1.a1', 'old_label': '12.r1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '12.r1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515055
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '16.a1', 'aut_quo_index': None, 'aut_stab_index': 16, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1', '4.b1.b1', '4.c1.a1'], 'contains': ['32.a1.a1', '48.r1.a1', '64.a1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [1429, -1, 8768, -1, 7674, -1, 7963, -1], 'generators': [1, 384, 2, 4, 480], 'label': '768.1088652.16.a1.a1', 'mobius_quo': None, 'mobius_sub': 2, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.a1.a1', 'old_label': '16.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515056
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '16.b1', 'aut_quo_index': None, 'aut_stab_index': 64, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.b1.a1'], 'contains': ['32.b2.a1', '48.s1.a1', '64.a1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 16, 'diagramx': [240, -1, 9977, -1, 9650, -1, 9266, -1], 'generators': [1, 24, 2, 4, 12], 'label': '768.1088652.16.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '16.b1.a1', 'old_label': '16.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515060
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.a1'], 'contains': ['48.a1.a1', '64.b1.a1', '64.c1.a1', '64.c2.a1', '64.c2.a2'], 'core': '48.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [953, -1, 6571, -1, 5626, -1, 9580, -1], 'generators': [4, 384, 36, 24, 480], 'label': '768.1088652.16.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '16.c1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68515061
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.a1', '12.h1.a1', '16.a1.a1', '16.b1.a1', '16.b1.a2'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [1243, -1, 8801, -1, 7782, -1, 8404, -1], 'generators': [1, 480, 24, 2, 384, 4, 12], 'label': '768.1088652.4.b1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.a1', 'old_label': '4.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68515062
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '16.c1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '192.955', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.a1.b1'], 'contains': ['48.a1.b1', '64.b1.a1', '64.c1.b1', '64.c2.b1', '64.c2.b2'], 'core': '48.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [953, -1, 5801, -1, 5626, -1, 8324, -1], 'generators': [4, 384, 468, 216, 480], 'label': '768.1088652.16.c1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '16.c1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.c1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68515063
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '16.d1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '192.956', 'aut_weyl_index': 32, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.b1.a1'], 'contains': ['48.b1.a1', '64.b1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [3617, -1, 776, -1, 502, -1, 6453, -1], 'generators': [4, 384, 48, 192, 96], 'label': '768.1088652.16.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '16.d1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.d1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68515064
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.5677', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '8.c1.a1'], 'contains': ['48.bu1.a1', '64.b1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 8, 'diagramx': [3864, -1, 1279, -1, 75, -1, 6564, -1], 'generators': [4, 384, 276, 552, 96], 'label': '768.1088652.16.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '8.c1.a1', 'old_label': '16.e1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1.a1', 'subgroup_fusion': None, 'weyl_group': '48.3'}
-
id: 68515065
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.a1', '12.h1.a1', '12.i1.b1'], 'contains': ['48.a1.a1', '48.i1.a1', '48.o1.a1', '48.w1.a1', '48.bb1.a1'], 'core': '24.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [1198, 7855, 7719, 9216, 7040, 5562, 7247, 6277], 'generators': [2, 12, 24, 384, 480], 'label': '768.1088652.24.a1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515066
{'ambient': '768.1088652', 'aut_centralizer_order': 64, 'aut_label': '24.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.a1.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.a1.b1', '12.h1.b1', '12.i1.a1'], 'contains': ['48.a1.b1', '48.i1.b1', '48.o1.b1', '48.w1.b1', '48.bb1.b1'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1198, 7855, 6887, 7206, 7040, 5562, 6660, 4666], 'generators': [2, 636, 600, 384, 480], 'label': '768.1088652.24.a1.b1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.a1.b1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.a1.b1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.a1.b1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.a1.b1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515067
{'ambient': '768.1088652', 'aut_centralizer_order': 128, 'aut_label': '24.b1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '48.48', 'aut_weyl_index': 128, 'centralizer': '24.b1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['8.b1.a1', '12.g1.a1', '12.k1.a1'], 'contains': ['48.b1.a1', '48.p1.a1', '48.bo1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [8054, 5103, 2679, 3333, 2171, 8372, 624, 8635], 'generators': [2, 624, 576], 'label': '768.1088652.24.b1.a1', 'mobius_quo': 0, 'mobius_sub': -12, 'normal_closure': '24.b1.a1', 'normal_contained_in': ['6.a1.a1'], 'normal_contains': ['48.b1.a1', '96.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '24.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': '24.12', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '24.b1.a1', 'subgroup_fusion': None, 'weyl_group': '24.12'}
-
id: 68515068
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.c1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.f1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1'], 'contains': ['48.c1.a1', '48.c1.b1', '48.e1.a1', '48.e1.b1', '48.g1.a1', '48.k1.a1', '48.m1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2585, -1, 7407, -1, 8370, -1, 6330, -1], 'generators': [385, 12, 624], 'label': '768.1088652.24.c1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.c1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515069
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.d1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.e1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1'], 'contains': ['48.c1.a1', '48.c1.b1', '48.d1.a1', '48.d1.b1', '48.g1.a1', '48.k1.a1', '48.l1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [2374, -1, 7506, -1, 8153, -1, 6769, -1], 'generators': [1, 12, 624], 'label': '768.1088652.24.d1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.d1.a1', 'old_label': '24.d1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.d1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515070
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.d1.a1', '48.f1.a1', '48.i1.a1', '48.s1.a1', '48.s1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [672, -1, 8944, -1, 9011, -1, 8556, -1], 'generators': [1, 24, 480], 'label': '768.1088652.24.e1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.e1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515071
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.e1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.d1.b1', '48.f1.b1', '48.i1.b1', '48.s1.b1', '48.s1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [672, -1, 8247, -1, 9011, -1, 7788, -1], 'generators': [1, 600, 480], 'label': '768.1088652.24.e1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.e1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.e1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515072
{'ambient': '768.1088652', 'aut_centralizer_order': 2, 'aut_label': '4.b1', 'aut_quo_index': None, 'aut_stab_index': 8, 'aut_weyl_group': '384.17948', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.a1.b1', '12.h1.b1', '16.a1.a1', '16.b1.b1', '16.b1.b2'], 'core': '24.a1.b1', 'coset_action_label': None, 'count': 4, 'diagramx': [1243, -1, 8691, -1, 7782, -1, 8143, -1], 'generators': [1, 480, 312, 2, 384, 4, 732], 'label': '768.1088652.4.b1.b1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.b1.b1', 'old_label': '4.b1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.b1.b1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68515073
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.a1'], 'contains': ['48.e1.a1', '48.f1.a1', '48.i1.a1', '48.bv1.a1', '48.bv1.a2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [916, -1, 8810, -1, 9309, -1, 8176, -1], 'generators': [385, 24, 480], 'label': '768.1088652.24.f1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.a1', 'old_label': '24.f1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.a1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515074
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.f1', 'aut_quo_index': None, 'aut_stab_index': 24, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.h1.b1'], 'contains': ['48.e1.b1', '48.f1.b1', '48.i1.b1', '48.bv1.b1', '48.bv1.b2'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [916, -1, 7816, -1, 9309, -1, 7565, -1], 'generators': [385, 600, 480], 'label': '768.1088652.24.f1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.h1.b1', 'old_label': '24.f1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.f1.b1', 'subgroup_fusion': None, 'weyl_group': '8.5'}
-
id: 68515075
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.g1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.j1.a1', '48.l1.a1', '48.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9571, -1, 5528, -1, 6339, -1, 346, -1], 'generators': [1, 588], 'label': '768.1088652.24.g1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.g1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.g1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515076
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.h1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.j1.a1'], 'contains': ['48.j1.a1', '48.m1.a1', '48.n1.a1'], 'core': '384.a1.a1', 'coset_action_label': None, 'count': 12, 'diagramx': [9694, -1, 5595, -1, 6484, -1, 255, -1], 'generators': [385, 588], 'label': '768.1088652.24.h1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '12.j1.a1', 'old_label': '24.h1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.h1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515077
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.g1.a1', '12.i1.b1'], 'contains': ['48.o1.a1', '48.p1.a1', '48.q1.a1', '48.bc1.a1', '48.bd1.a1', '48.bi1.b1', '48.bj1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7092, -1, 4064, -1, 3114, -1, 1545, -1], 'generators': [2, 12, 576], 'label': '768.1088652.24.i1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.i1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515078
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.i1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '16.14', 'aut_weyl_index': 384, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.g1.a1', '12.i1.a1'], 'contains': ['48.o1.b1', '48.p1.a1', '48.q1.a1', '48.bc1.b1', '48.bd1.b1', '48.bi1.a1', '48.bj1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7092, -1, 3928, -1, 3114, -1, 1359, -1], 'generators': [2, 636, 576], 'label': '768.1088652.24.i1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.i1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.i1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515079
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.c1.a1', '12.i1.b1'], 'contains': ['48.o1.a1', '48.q1.a1', '48.be1.a1', '48.bf1.a1', '48.bk1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5698, -1, 4726, -1, 3962, -1, 4367, -1], 'generators': [2, 12, 648], 'label': '768.1088652.24.j1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515080
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.j1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.c1.a1', '12.i1.a1'], 'contains': ['48.o1.b1', '48.q1.a1', '48.be1.b1', '48.bf1.b1', '48.bk1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [5698, -1, 4198, -1, 3962, -1, 3497, -1], 'generators': [2, 636, 456], 'label': '768.1088652.24.j1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.j1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.j1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515081
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.d1.a1', '12.h1.a1'], 'contains': ['48.c1.a1', '48.d1.a1', '48.e1.a1', '48.o1.a1', '48.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1653, -1, 8085, -1, 8627, -1, 7380, -1], 'generators': [1, 12, 384], 'label': '768.1088652.24.k1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.k1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515082
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.k1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.d1.a1', '12.h1.b1'], 'contains': ['48.c1.b1', '48.d1.b1', '48.e1.b1', '48.o1.b1', '48.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1653, -1, 7622, -1, 8627, -1, 6929, -1], 'generators': [1, 636, 384], 'label': '768.1088652.24.k1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.k1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.k1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515083
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '4.c1', 'aut_quo_index': None, 'aut_stab_index': 4, 'aut_weyl_group': '384.17949', 'aut_weyl_index': 16, 'centralizer': '384.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['8.b1.a1', '12.k1.a1', '16.a1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 4, 'diagramx': [4030, -1, 5753, -1, 5169, -1, 6464, -1], 'generators': [1, 480, 576, 2, 384, 4, 624], 'label': '768.1088652.4.c1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.c1.a1', 'old_label': '4.c1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.c1.a1', 'subgroup_fusion': None, 'weyl_group': '96.64'}
-
id: 68515084
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.a1', '12.e1.b1', '12.h1.a1'], 'contains': ['48.f1.a1', '48.o1.a1', '48.t1.a1', '48.bl1.b1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1896, -1, 7950, -1, 7896, -1, 7115, -1], 'generators': [25, 12, 384], 'label': '768.1088652.24.l1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.b1', 'old_label': '24.l1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515085
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.l1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.b1.b1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.b1.b1', '12.e1.a1', '12.h1.b1'], 'contains': ['48.f1.b1', '48.o1.b1', '48.t1.b1', '48.bl1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [1896, -1, 6983, -1, 7896, -1, 6169, -1], 'generators': [601, 636, 384], 'label': '768.1088652.24.l1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.d1.a1', 'old_label': '24.l1.b1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.l1.b1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515086
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.m1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.e1.a1', '12.e1.b1', '12.f1.a1', '12.g1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['48.g1.a1', '48.o1.a1', '48.o1.b1', '48.p1.a1', '48.u1.a1', '48.z1.a1', '48.z1.b1', '48.bg1.a1', '48.bm1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [3277, -1, 6111, -1, 6141, -1, 5490, -1], 'generators': [2, 12, 624, 384], 'label': '768.1088652.24.m1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.m1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.m1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515087
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.n1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.27', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.i1.a1', '12.i1.b1'], 'contains': ['48.h1.a1', '48.o1.a1', '48.o1.b1', '48.q1.a1', '48.v1.a1', '48.ba1.a1', '48.ba1.b1', '48.bh1.a1', '48.bn1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5202, -1, 4850, -1, 5060, -1, 5334, -1], 'generators': [2, 12, 600, 384], 'label': '768.1088652.24.n1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.n1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.n1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515088
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.o1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.g1.a1', '12.j1.a1'], 'contains': ['48.j1.a1', '48.p1.a1', '48.q1.a1', '48.x1.a1', '48.bp1.a1', '48.bq1.a1', '48.br1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9398, -1, 3805, -1, 2566, -1, 469, -1], 'generators': [2, 588, 624, 384], 'label': '768.1088652.24.o1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.o1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.o1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515089
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.p1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.d1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.k1.a1', '48.l1.a1', '48.m1.a1', '48.p1.a1', '48.r1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [3493, -1, 5693, -1, 7462, -1, 5767, -1], 'generators': [1, 624, 384], 'label': '768.1088652.24.p1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.p1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.p1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515090
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.q1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '32.46', 'aut_weyl_index': 192, 'centralizer': '96.c1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.j1.a1', '12.k1.a1'], 'contains': ['48.n1.a1', '48.p1.a1', '48.y1.a1', '48.bs1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [9917, -1, 5416, -1, 5360, -1, 100, -1], 'generators': [577, 624, 384], 'label': '768.1088652.24.q1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.b1.a1', 'old_label': '24.q1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.q1.a1', 'subgroup_fusion': None, 'weyl_group': '16.11'}
-
id: 68515091
{'ambient': '768.1088652', 'aut_centralizer_order': 32, 'aut_label': '24.r1', 'aut_quo_index': None, 'aut_stab_index': 2, 'aut_weyl_group': '96.195', 'aut_weyl_index': 64, 'centralizer': '24.r1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['8.c1.a1', '12.c1.a1'], 'contains': ['48.q1.a1', '48.bt1.a1', '48.bu1.a1'], 'core': '96.a1.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [8837, -1, 521, -1, 288, -1, 2551, -1], 'generators': [2, 588, 456], 'label': '768.1088652.24.r1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.a1.a1', 'old_label': '24.r1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.r1.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
-
id: 68515092
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.p1.b1'], 'contains': ['48.z1.a1', '48.bc1.a1', '48.bd1.a1', '48.bi1.a1', '48.bj1.a1', '48.bo1.a1', '48.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7610, -1, 2894, -1, 1828, -1, 747, -1], 'generators': [626, 12, 576], 'label': '768.1088652.24.s1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.s1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515093
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.s1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.z1.b1', '48.bc1.b1', '48.bd1.b1', '48.bi1.b1', '48.bj1.b1', '48.bo1.a1', '48.br1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7610, -1, 2351, -1, 1828, -1, 1222, -1], 'generators': [626, 636, 576], 'label': '768.1088652.24.s1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.s1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.s1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515094
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '768.1087581', 'aut_weyl_index': 8, 'centralizer': '96.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.a1'], 'contains': ['12.a1.a1', '12.c1.a1', '12.g1.a1', '12.i1.a1', '12.i1.b1', '12.m1.a1', '12.n1.a1', '12.p1.a1', '12.p1.b1'], 'core': '6.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5892, 5356, 2974, 6372, 2427, 6171, 3724, 5688], 'generators': [2, 12, 24, 576, 624], 'label': '768.1088652.6.a1.a1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.a1', '24.a1.a1', '24.a1.b1', '24.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.a1.a1', 'subgroup_fusion': None, 'weyl_group': '96.227'}
-
id: 68515095
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.n1.a1', '12.p1.b1'], 'contains': ['48.ba1.a1', '48.bc1.a1', '48.bf1.a1', '48.bi1.a1', '48.bk1.a1', '48.bq1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6424, -1, 1264, -1, 1392, -1, 2045, -1], 'generators': [650, 12, 576], 'label': '768.1088652.24.t1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.t1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515096
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.t1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.n1.a1', '12.p1.a1'], 'contains': ['48.ba1.b1', '48.bc1.b1', '48.bf1.b1', '48.bi1.b1', '48.bk1.b1', '48.bq1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6424, -1, 961, -1, 1392, -1, 2316, -1], 'generators': [650, 636, 576], 'label': '768.1088652.24.t1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.t1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.t1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515097
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1', '12.p1.b1'], 'contains': ['48.ba1.a1', '48.bd1.a1', '48.be1.a1', '48.bj1.a1', '48.bk1.a1', '48.br1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7414, -1, 2161, -1, 1537, -1, 1773, -1], 'generators': [578, 12, 648], 'label': '768.1088652.24.u1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.u1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515098
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.u1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.267', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.ba1.b1', '48.bd1.b1', '48.be1.b1', '48.bj1.b1', '48.bk1.b1', '48.br1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7414, -1, 1330, -1, 1537, -1, 2135, -1], 'generators': [578, 636, 456], 'label': '768.1088652.24.u1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.u1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.u1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515099
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.a1', '12.l1.a1', '12.o1.a1'], 'contains': ['48.z1.a1', '48.bl1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2954, -1, 6371, -1, 6825, -1, 4687, -1], 'generators': [601, 12], 'label': '768.1088652.24.v1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '24.v1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515100
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.v1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.e1.b1', '12.l1.b1', '12.o1.b1'], 'contains': ['48.z1.b1', '48.bl1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [2954, -1, 6290, -1, 6825, -1, 5909, -1], 'generators': [25, 636], 'label': '768.1088652.24.v1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.v1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.v1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515101
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.a1', '12.o1.a1'], 'contains': ['48.z1.a1', '48.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6053, -1, 6209, -1, 6647, -1, 849, -1], 'generators': [577, 12], 'label': '768.1088652.24.w1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.b1', 'old_label': '24.w1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.a1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515102
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.w1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '64.138', 'aut_weyl_index': 96, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.f1.a1', '12.l1.b1', '12.o1.b1'], 'contains': ['48.z1.b1', '48.bs1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6053, -1, 6014, -1, 6647, -1, 2418, -1], 'generators': [577, 636], 'label': '768.1088652.24.w1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.e1.a1', 'old_label': '24.w1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.w1.b1', 'subgroup_fusion': None, 'weyl_group': '32.6'}
-
id: 68515103
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.ba1.a1', '48.bb1.a1', '48.bc1.a1', '48.bi1.b1', '48.bk1.b1', '48.bm1.a1', '48.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5419, -1, 2560, -1, 2828, -1, 2976, -1], 'generators': [26, 12, 576], 'label': '768.1088652.24.x1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.x1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515104
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.x1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.n1.a1'], 'contains': ['48.ba1.b1', '48.bb1.b1', '48.bc1.b1', '48.bi1.a1', '48.bk1.a1', '48.bm1.a1', '48.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [5419, -1, 2256, -1, 2828, -1, 3147, -1], 'generators': [26, 636, 576], 'label': '768.1088652.24.x1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.x1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.x1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515105
{'ambient': '768.1088652', 'aut_centralizer_order': 4, 'aut_label': '6.b1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '512.7530050', 'aut_weyl_index': 12, 'centralizer': '192.b1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1'], 'contains': ['12.d1.a1', '12.f1.a1', '12.g1.a1', '12.j1.a1', '12.k1.a1'], 'core': '24.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6720, -1, 5856, -1, 5634, -1, 1705, -1], 'generators': [1, 12, 576], 'label': '768.1088652.6.b1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '6.b1.a1', 'projective_image': '384.18135', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.b1.a1', 'subgroup_fusion': None, 'weyl_group': '64.138'}
-
id: 68515106
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.l1.a1', '12.m1.a1'], 'contains': ['48.z1.a1', '48.bb1.a1', '48.be1.a1', '48.bj1.b1', '48.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4762, -1, 4597, -1, 4523, -1, 3846, -1], 'generators': [626, 12, 648], 'label': '768.1088652.24.y1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515107
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.y1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.l1.b1', '12.m1.a1'], 'contains': ['48.z1.b1', '48.bb1.b1', '48.be1.b1', '48.bj1.a1', '48.bn1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4762, -1, 4462, -1, 4523, -1, 4017, -1], 'generators': [626, 636, 456], 'label': '768.1088652.24.y1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.y1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.y1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515108
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.n1.a1', '12.p1.b1'], 'contains': ['48.ba1.a1', '48.bb1.b1', '48.bf1.b1', '48.bg1.a1', '48.bi1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4537, -1, 3436, -1, 4248, -1, 3318, -1], 'generators': [602, 12, 624], 'label': '768.1088652.24.z1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515109
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.z1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '64.202', 'aut_weyl_index': 96, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.n1.a1', '12.p1.a1'], 'contains': ['48.ba1.b1', '48.bb1.a1', '48.bf1.a1', '48.bg1.a1', '48.bi1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4537, -1, 3180, -1, 4248, -1, 4545, -1], 'generators': [26, 12, 624], 'label': '768.1088652.24.z1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.z1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.z1.b1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515110
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.a1', '12.m1.a1', '12.p1.b1'], 'contains': ['48.z1.a1', '48.ba1.a1', '48.bb1.b1', '48.bd1.b1', '48.bh1.a1', '48.bj1.a1', '48.bk1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4987, -1, 3561, -1, 3676, -1, 2805, -1], 'generators': [626, 12, 600], 'label': '768.1088652.24.ba1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.ba1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515111
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.ba1', 'aut_quo_index': None, 'aut_stab_index': 12, 'aut_weyl_group': '32.51', 'aut_weyl_index': 192, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.i1.b1', '12.m1.a1', '12.p1.a1'], 'contains': ['48.z1.b1', '48.ba1.b1', '48.bb1.a1', '48.bd1.a1', '48.bh1.a1', '48.bj1.b1', '48.bk1.b1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [4987, -1, 3055, -1, 3676, -1, 4189, -1], 'generators': [578, 12, 600], 'label': '768.1088652.24.ba1.b1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.ba1.b1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.ba1.b1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515112
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bb1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.g1.a1', '12.p1.a1', '12.p1.b1'], 'contains': ['48.bd1.a1', '48.bd1.b1', '48.bg1.a1', '48.bo1.a1', '48.bq1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9115, -1, 3275, -1, 2368, -1, 1041, -1], 'generators': [578, 12, 624], 'label': '768.1088652.24.bb1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bb1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bb1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515113
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.bc1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.c1.a1', '12.m1.a1'], 'contains': ['48.bc1.a1', '48.bc1.b1', '48.be1.a1', '48.be1.b1', '48.bh1.a1', '48.bp1.a1', '48.bu1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [6186, -1, 676, -1, 665, -1, 2674, -1], 'generators': [12, 648, 576], 'label': '768.1088652.24.bc1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.bc1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bc1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
-
id: 68515114
{'ambient': '768.1088652', 'aut_centralizer_order': 16, 'aut_label': '24.bd1', 'aut_quo_index': None, 'aut_stab_index': 3, 'aut_weyl_group': '128.1755', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.a1.a1', '12.g1.a1', '12.n1.a1'], 'contains': ['48.b1.a1', '48.bc1.a1', '48.bc1.b1', '48.bg1.a1', '48.bp1.a1'], 'core': '48.b1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [6305, -1, 611, -1, 810, -1, 1863, -1], 'generators': [12, 624, 576], 'label': '768.1088652.24.bd1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '12.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '24.bd1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.bd1.a1', 'subgroup_fusion': None, 'weyl_group': '32.27'}
-
id: 68515115
{'ambient': '768.1088652', 'aut_centralizer_order': 8, 'aut_label': '24.be1', 'aut_quo_index': None, 'aut_stab_index': 6, 'aut_weyl_group': '128.1578', 'aut_weyl_index': 48, 'centralizer': '96.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['12.c1.a1', '12.p1.a1', '12.p1.b1'], 'contains': ['48.bd1.a1', '48.bd1.b1', '48.bf1.a1', '48.bf1.b1', '48.bh1.a1', '48.br1.a1', '48.bt1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 6, 'diagramx': [7848, -1, 2465, -1, 1246, -1, 2226, -1], 'generators': [434, 12, 600], 'label': '768.1088652.24.be1.a1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '6.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '6.a1.a1', 'old_label': '24.be1.a1', 'projective_image': '768.1088652', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24.be1.a1', 'subgroup_fusion': None, 'weyl_group': '16.14'}
