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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.1400', 'ambient_counter': 1400, 'ambient_order': 192, 'ambient_tex': 'C_2^2\\times C_4\\times C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 192, 'characteristic': True, 'core_order': 192, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '192.1400.1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1.a1', 'outer_equivalence': True, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['Z', 'F', 'R', 'U0', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.1400', 'subgroup_hash': 1400, 'subgroup_order': 192, 'subgroup_tex': 'C_2^2\\times C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '192.1400', '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': '1.a1', 'complements': ['192.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1', '2.b1', '3.a1'], 'core': '1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6749, 6749, 5579, 5579], 'generators': [1, 8, 64, 2, 96, 4, 48], 'label': '192.1400.1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1', '2.b1', '3.a1'], 'normalizer': '1.a1', 'old_label': '1.a1', 'projective_image': '1.1', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '192.1400', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 2], 'aut_gens': [[1, 2, 4, 16], [1, 2, 4, 112], [1, 2, 100, 16], [97, 2, 100, 16], [1, 2, 4, 80], [1, 2, 52, 16], [1, 2, 12, 16], [1, 98, 100, 16], [9, 2, 12, 16], [1, 2, 4, 24], [11, 97, 152, 31], [1, 10, 12, 16], [3, 2, 6, 80]], 'aut_group': '294912.rz', 'aut_hash': 8959512375774918584, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 294912, 'aut_permdeg': 50, 'aut_perms': [1901916663400722826898695024075585595263006024952538324141446400, 2591857379618860401645155279731049775443259472271963802285504, 3149851289675655121459685651123013699790979866399173585567680064, 1, 610378974783133799541153731228236503011233708950621158991228744, 847253356555579268804166755172965034654916795738549488, 2528889627065643308048661212341431446628674420568973068598428144, 3054155069983822766275545566900390125586889654569397327637690128, 1837519476872398335794672282144131706797313879815678555940442960, 1733872621475016805663274407559618897212203430357522092671285166, 2445866063113418131691765795300529852057070498407340424926035888, 1677431787779880944336231424539669472444868517919670324320], 'aut_phi_ratio': 4608.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 12, 1], [3, 1, 2, 1], [4, 1, 48, 1], [6, 1, 6, 1], [6, 1, 24, 1], [12, 1, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^9.\\POPlus(4,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '294912.rz', 'autcent_hash': 8959512375774918584, 'autcent_nilpotent': False, 'autcent_order': 294912, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^9.\\POPlus(4,3)', '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], [2, 1, 15], [3, 1, 2], [4, 1, 48], [6, 1, 30], [12, 1, 96]], 'center_label': '192.1400', 'center_order': 192, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1400, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1], ['4.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [3, 1, 2, 1], [4, 1, 2, 24], [6, 1, 2, 15], [12, 1, 4, 24]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1400, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '48.52', 'hash': 1400, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 16], [1, 2, 4, 16], [1, 2, 4, 16], [1, 2, 4, 16]], '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, 192]], 'label': '192.1400', 'linC_count': None, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C4*C12', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 192, 'number_divisions': 80, 'number_normal_subgroups': 498, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 498, 'number_subgroups': 498, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 48], [6, 30], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 112], [1, 2, 100, 16], [97, 2, 100, 16], [1, 2, 4, 80], [1, 2, 52, 16], [1, 2, 12, 16], [1, 98, 100, 16], [9, 2, 12, 16], [1, 2, 4, 24], [11, 97, 152, 31], [1, 10, 12, 16], [3, 2, 6, 80]], 'outer_group': '294912.rz', 'outer_hash': 8959512375774918584, 'outer_nilpotent': False, 'outer_order': 294912, 'outer_permdeg': 50, 'outer_perms': [1901916663400722826898695024075585595263006024952538324141446400, 2591857379618860401645155279731049775443259472271963802285504, 3149851289675655121459685651123013699790979866399173585567680064, 1, 610378974783133799541153731228236503011233708950621158991228744, 847253356555579268804166755172965034654916795738549488, 2528889627065643308048661212341431446628674420568973068598428144, 3054155069983822766275545566900390125586889654569397327637690128, 1837519476872398335794672282144131706797313879815678555940442960, 1733872621475016805663274407559618897212203430357522092671285166, 2445866063113418131691765795300529852057070498407340424926035888, 1677431787779880944336231424539669472444868517919670324320], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^9.\\POPlus(4,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 4, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 40], [4, 24]], 'representations': {'PC': {'code': 643420460685825, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 58, 102, 124]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083311105, 1118833793, 40044672, 2149582850, 3260482691, 1087570945, 44304512]}, 'Perm': {'d': 15, 'gens': [11612160, 2400, 87178291200, 479001600, 4, 3669120, 744]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4, 12], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_4\\times C_{12}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '192.1400', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 2], 'aut_gens': [[1, 2, 4, 16], [1, 2, 4, 112], [1, 2, 100, 16], [97, 2, 100, 16], [1, 2, 4, 80], [1, 2, 52, 16], [1, 2, 12, 16], [1, 98, 100, 16], [9, 2, 12, 16], [1, 2, 4, 24], [11, 97, 152, 31], [1, 10, 12, 16], [3, 2, 6, 80]], 'aut_group': '294912.rz', 'aut_hash': 8959512375774918584, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 294912, 'aut_permdeg': 50, 'aut_perms': [1901916663400722826898695024075585595263006024952538324141446400, 2591857379618860401645155279731049775443259472271963802285504, 3149851289675655121459685651123013699790979866399173585567680064, 1, 610378974783133799541153731228236503011233708950621158991228744, 847253356555579268804166755172965034654916795738549488, 2528889627065643308048661212341431446628674420568973068598428144, 3054155069983822766275545566900390125586889654569397327637690128, 1837519476872398335794672282144131706797313879815678555940442960, 1733872621475016805663274407559618897212203430357522092671285166, 2445866063113418131691765795300529852057070498407340424926035888, 1677431787779880944336231424539669472444868517919670324320], 'aut_phi_ratio': 4608.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 12, 1], [3, 1, 2, 1], [4, 1, 48, 1], [6, 1, 6, 1], [6, 1, 24, 1], [12, 1, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^9.\\POPlus(4,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '294912.rz', 'autcent_hash': 8959512375774918584, 'autcent_nilpotent': False, 'autcent_order': 294912, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^9.\\POPlus(4,3)', '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], [2, 1, 15], [3, 1, 2], [4, 1, 48], [6, 1, 30], [12, 1, 96]], 'center_label': '192.1400', 'center_order': 192, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1400, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['3.1', 1], ['4.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [3, 1, 2, 1], [4, 1, 2, 24], [6, 1, 2, 15], [12, 1, 4, 24]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1400, 'exponent': 12, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '48.52', 'hash': 1400, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 16], [1, 2, 4, 16], [1, 2, 4, 16], [1, 2, 4, 16]], '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, 192]], 'label': '192.1400', 'linC_count': None, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C4*C12', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 192, 'number_divisions': 80, 'number_normal_subgroups': 498, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 498, 'number_subgroups': 498, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 48], [6, 30], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 2, 4, 2, 2, 2, 2, 6, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 4, 112], [1, 2, 100, 16], [97, 2, 100, 16], [1, 2, 4, 80], [1, 2, 52, 16], [1, 2, 12, 16], [1, 98, 100, 16], [9, 2, 12, 16], [1, 2, 4, 24], [11, 97, 152, 31], [1, 10, 12, 16], [3, 2, 6, 80]], 'outer_group': '294912.rz', 'outer_hash': 8959512375774918584, 'outer_nilpotent': False, 'outer_order': 294912, 'outer_permdeg': 50, 'outer_perms': [1901916663400722826898695024075585595263006024952538324141446400, 2591857379618860401645155279731049775443259472271963802285504, 3149851289675655121459685651123013699790979866399173585567680064, 1, 610378974783133799541153731228236503011233708950621158991228744, 847253356555579268804166755172965034654916795738549488, 2528889627065643308048661212341431446628674420568973068598428144, 3054155069983822766275545566900390125586889654569397327637690128, 1837519476872398335794672282144131706797313879815678555940442960, 1733872621475016805663274407559618897212203430357522092671285166, 2445866063113418131691765795300529852057070498407340424926035888, 1677431787779880944336231424539669472444868517919670324320], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^9.\\POPlus(4,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 4, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 40], [4, 24]], 'representations': {'PC': {'code': 643420460685825, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 58, 102, 124]}, 'GLFq': {'d': 4, 'q': 4, 'gens': [1083311105, 1118833793, 40044672, 2149582850, 3260482691, 1087570945, 44304512]}, 'Perm': {'d': 15, 'gens': [11612160, 2400, 87178291200, 479001600, 4, 3669120, 744]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4, 12], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_4\\times C_{12}', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
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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}
