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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '3080.a', 'ambient_counter': 1, 'ambient_order': 3080, 'ambient_tex': 'C_{11}\\times D_{140}', 'central': True, 'central_factor': False, 'centralizer_order': 3080, 'characteristic': True, 'core_order': 1, 'counter': 64, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '3080.a.3080.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '3080.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '3080.a', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 2990120942828086407, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 3080, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{11}\\times D_{140}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C6'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '3080.a', 'aut_centralizer_order': None, 'aut_label': '3080.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': ['280.a1.a1', '440.a1.a1', '616.a1.a1', '1540.a1.a1', '1540.b1.a1', '1540.b1.b1'], 'contains': [], 'core': '3080.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2153, 7474, 7809, 4323, 3339, 3537, 3212, 3938], 'generators': [], 'label': '3080.a.3080.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '3080.a1.a1', 'normal_contained_in': ['280.a1.a1', '440.a1.a1', '616.a1.a1', '1540.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '3080.a1.a1', 'projective_image': '3080.a', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '3080.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '44.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 60, 30, 60, 60, 60], 'aut_gens': [[1, 2], [1783, 2026], [1761, 1086], [793, 1802], [1805, 2986], [2531, 1114], [3059, 2766]], 'aut_group': None, 'aut_hash': 2583246734037088748, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 67200, 'aut_permdeg': 150, 'aut_perms': [31190434095692593744297498716403222744888678740119029611507246383812932599510064764390326058352585644097458728326575167989794635512817408091085604795366953540984801858736431034733479110060091003172205448246791212486709392952023869017077571577707282884361100778549, 2860813496049147950713958491619252943327318300757234757544628015458671289678268640284353886564208610930857009799805923254450179508569061211030205296075978973767111872766472858673595592602375952211907005731197375396759734018540666206296348323303555091918580692924, 4880092764129751917235611303724206144798416035201531289627710927692316575132880856582552763570853869130440656332669452265339332284077348842223801712832750851253395972668351907723788914822828449239453714192980852391902703099595296079274768690183119133160401937060, 28336238138524514209870865326907097793026198193277186050496417577852420083921383770675582964888789332627019575392210428677923480314719809467060902135359928598130297435647679777364549031595715231562103039743614237936188421520206361390545039621989453022305761935051, 7147009198114266339787186901816789523293345298658209934154420798586544541494638283900089521082680241090259958804104636239169746087654648394747055931900793579979605693846856392891853457524494477026477729795739880618495142199817833790622141181501900064406958279508, 50589580640508809136350438783740792732145669208009300485550626973061982147788792470034252831865072659924708849913973620888252942545334343005832674044462916818715796899954965069663971865715842379122066013767454772184980475332965504339074562786072269759021232773889], 'aut_phi_ratio': 70.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 70, 2, 1], [4, 2, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [20, 2, 4, 1], [22, 1, 10, 1], [22, 70, 20, 1], [28, 2, 6, 1], [35, 2, 12, 1], [44, 2, 10, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [220, 2, 40, 1], [308, 2, 60, 1], [385, 2, 120, 1], [770, 2, 120, 1], [1540, 2, 240, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{70}.C_{30}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '40.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '1680.934', 'autcentquo_hash': 934, 'autcentquo_nilpotent': False, 'autcentquo_order': 1680, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{70}:C_{12}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 70, 2], [4, 2, 1], [5, 2, 2], [7, 2, 3], [10, 2, 2], [11, 1, 10], [14, 2, 3], [20, 2, 4], [22, 1, 10], [22, 70, 20], [28, 2, 6], [35, 2, 12], [44, 2, 10], [55, 2, 20], [70, 2, 12], [77, 2, 30], [110, 2, 20], [140, 2, 24], [154, 2, 30], [220, 2, 40], [308, 2, 60], [385, 2, 120], [770, 2, 120], [1540, 2, 240]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '140.10', 'commutator_count': 1, 'commutator_label': '70.4', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '7.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['280.26', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 70, 1, 2], [4, 2, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [20, 2, 4, 1], [22, 1, 10, 1], [22, 70, 10, 2], [28, 2, 6, 1], [35, 2, 12, 1], [44, 2, 10, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [220, 2, 40, 1], [308, 2, 60, 1], [385, 2, 120, 1], [770, 2, 120, 1], [1540, 2, 240, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 1540, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7, 11], 'faithful_reps': [[2, 0, 240]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1540.34', 'hash': 2990120942828086407, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 70], 'inner_gens': [[1, 838], [2245, 2]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 140, 'inner_split': True, 'inner_tex': 'D_{70}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 480, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 44], [2, 759]], 'label': '3080.a', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11*D140', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 803, 'number_divisions': 28, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 64, 'number_subgroups': 696, 'old_label': None, 'order': 3080, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 141], [4, 2], [5, 4], [7, 6], [10, 4], [11, 10], [14, 6], [20, 8], [22, 1410], [28, 12], [35, 24], [44, 20], [55, 40], [70, 24], [77, 60], [110, 40], [140, 48], [154, 60], [220, 80], [308, 120], [385, 240], [770, 240], [1540, 480]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 2, 2, 60], 'outer_gen_pows': [3010, 0, 0, 0], 'outer_gens': [[771, 2242], [1, 2242], [1, 1542], [1, 1194]], 'outer_group': '480.1180', 'outer_hash': 1180, 'outer_nilpotent': True, 'outer_order': 480, 'outer_permdeg': 18, 'outer_perms': [355687428096000, 1307761459200, 6227020800, 6270935073], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{60}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 1], [4, 2], [6, 2], [8, 1], [10, 4], [12, 1], [20, 1], [24, 2], [40, 2], [48, 1], [60, 2], [80, 1], [120, 1], [240, 2], [480, 1]], 'representations': {'PC': {'code': '162935777803183390649179119288830000359', 'gens': [1, 2], 'pres': [6, -2, -2, -2, -5, -7, -11, 10057, 31, 30170, 50, 6531, 141, 40804, 238]}, 'GLFp': {'d': 2, 'p': 419, 'gens': [30748104663, 17334066269]}, 'Perm': {'d': 27, 'gens': [87181961047, 419450149241385347098622197]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 22], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\times D_{140}', 'transitive_degree': 1540, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '44.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 60, 30, 60, 60, 60], 'aut_gens': [[1, 2], [1783, 2026], [1761, 1086], [793, 1802], [1805, 2986], [2531, 1114], [3059, 2766]], 'aut_group': None, 'aut_hash': 2583246734037088748, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 67200, 'aut_permdeg': 150, 'aut_perms': [31190434095692593744297498716403222744888678740119029611507246383812932599510064764390326058352585644097458728326575167989794635512817408091085604795366953540984801858736431034733479110060091003172205448246791212486709392952023869017077571577707282884361100778549, 2860813496049147950713958491619252943327318300757234757544628015458671289678268640284353886564208610930857009799805923254450179508569061211030205296075978973767111872766472858673595592602375952211907005731197375396759734018540666206296348323303555091918580692924, 4880092764129751917235611303724206144798416035201531289627710927692316575132880856582552763570853869130440656332669452265339332284077348842223801712832750851253395972668351907723788914822828449239453714192980852391902703099595296079274768690183119133160401937060, 28336238138524514209870865326907097793026198193277186050496417577852420083921383770675582964888789332627019575392210428677923480314719809467060902135359928598130297435647679777364549031595715231562103039743614237936188421520206361390545039621989453022305761935051, 7147009198114266339787186901816789523293345298658209934154420798586544541494638283900089521082680241090259958804104636239169746087654648394747055931900793579979605693846856392891853457524494477026477729795739880618495142199817833790622141181501900064406958279508, 50589580640508809136350438783740792732145669208009300485550626973061982147788792470034252831865072659924708849913973620888252942545334343005832674044462916818715796899954965069663971865715842379122066013767454772184980475332965504339074562786072269759021232773889], 'aut_phi_ratio': 70.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 70, 2, 1], [4, 2, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [20, 2, 4, 1], [22, 1, 10, 1], [22, 70, 20, 1], [28, 2, 6, 1], [35, 2, 12, 1], [44, 2, 10, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [220, 2, 40, 1], [308, 2, 60, 1], [385, 2, 120, 1], [770, 2, 120, 1], [1540, 2, 240, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{70}.C_{30}.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '40.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '1680.934', 'autcentquo_hash': 934, 'autcentquo_nilpotent': False, 'autcentquo_order': 1680, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_{70}:C_{12}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 70, 2], [4, 2, 1], [5, 2, 2], [7, 2, 3], [10, 2, 2], [11, 1, 10], [14, 2, 3], [20, 2, 4], [22, 1, 10], [22, 70, 20], [28, 2, 6], [35, 2, 12], [44, 2, 10], [55, 2, 20], [70, 2, 12], [77, 2, 30], [110, 2, 20], [140, 2, 24], [154, 2, 30], [220, 2, 40], [308, 2, 60], [385, 2, 120], [770, 2, 120], [1540, 2, 240]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '140.10', 'commutator_count': 1, 'commutator_label': '70.4', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '7.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['280.26', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 70, 1, 2], [4, 2, 1, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [20, 2, 4, 1], [22, 1, 10, 1], [22, 70, 10, 2], [28, 2, 6, 1], [35, 2, 12, 1], [44, 2, 10, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [140, 2, 24, 1], [154, 2, 30, 1], [220, 2, 40, 1], [308, 2, 60, 1], [385, 2, 120, 1], [770, 2, 120, 1], [1540, 2, 240, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 1540, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7, 11], 'faithful_reps': [[2, 0, 240]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1540.34', 'hash': 2990120942828086407, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 70], 'inner_gens': [[1, 838], [2245, 2]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 140, 'inner_split': True, 'inner_tex': 'D_{70}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 480, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 44], [2, 759]], 'label': '3080.a', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11*D140', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 803, 'number_divisions': 28, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 64, 'number_subgroups': 696, 'old_label': None, 'order': 3080, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 141], [4, 2], [5, 4], [7, 6], [10, 4], [11, 10], [14, 6], [20, 8], [22, 1410], [28, 12], [35, 24], [44, 20], [55, 40], [70, 24], [77, 60], [110, 40], [140, 48], [154, 60], [220, 80], [308, 120], [385, 240], [770, 240], [1540, 480]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 2, 2, 60], 'outer_gen_pows': [3010, 0, 0, 0], 'outer_gens': [[771, 2242], [1, 2242], [1, 1542], [1, 1194]], 'outer_group': '480.1180', 'outer_hash': 1180, 'outer_nilpotent': True, 'outer_order': 480, 'outer_permdeg': 18, 'outer_perms': [355687428096000, 1307761459200, 6227020800, 6270935073], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{60}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 1], [4, 2], [6, 2], [8, 1], [10, 4], [12, 1], [20, 1], [24, 2], [40, 2], [48, 1], [60, 2], [80, 1], [120, 1], [240, 2], [480, 1]], 'representations': {'PC': {'code': '162935777803183390649179119288830000359', 'gens': [1, 2], 'pres': [6, -2, -2, -2, -5, -7, -11, 10057, 31, 30170, 50, 6531, 141, 40804, 238]}, 'GLFp': {'d': 2, 'p': 419, 'gens': [30748104663, 17334066269]}, 'Perm': {'d': 27, 'gens': [87181961047, 419450149241385347098622197]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 22], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\times D_{140}', 'transitive_degree': 1540, 'wreath_data': None, 'wreath_product': False}
