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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '288.402', 'ambient_counter': 402, 'ambient_order': 288, 'ambient_tex': 'C_{12}.S_4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '288.402.1.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': '288.402', 'subgroup_hash': 402, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '288.402', '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': '72.a1.a1', 'complements': ['288.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '3.a1.a1', '3.b1.a1', '3.b1.b1', '3.b1.c1', '4.b1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4721, 6241, 6940, 6392, 4559, 5782, 2823, 5793], 'generators': [1, 72, 48, 2, 144, 4, 8], 'label': '288.402.1.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': '72.43', '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': '72.43'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 8, 24, 144], [1, 8, 120, 144], [1, 16, 264, 144], [5, 8, 24, 144], [3, 8, 24, 144], [17, 8, 240, 216], [1, 104, 24, 144], [97, 8, 24, 144], [145, 224, 24, 144], [1, 80, 24, 144]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 72, 'aut_perms': [119104705619027829844289178024814194513020478876369172124638547721852809628426350200428029393631480, 6687643986850360475654769195338544889865432588698746975766707676481998180378565267642745007053430261, 8660026160654545993497270522209617247234983506768878788514676312025730343415543563822165298666347285781, 850828275212888371529444618539791166389365013336357835391274953932372908499614381585320177908853056816, 54362126952738340082700119758818943227791612403186596018643932385778641690507318750799517481762388994821, 4179761570608096679640365515766386688679288070613192003882467622360053352082839731583305361176904749, 20703151596379842745272631824867081493094904514533303865098858161807998727690135690723645150657655060576, 7786418879759582050403610847495620409648400786952607025511847971440210103549669995229765083468794493090, 6608255365820604288783102863724654969802626227039130111707139180693950712717615834214207398259609069], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 3, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 3, 1], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 8, 3], [4, 1, 2], [4, 3, 2], [6, 2, 1], [6, 6, 2], [6, 8, 3], [8, 18, 8], [12, 2, 2], [12, 6, 2], [12, 8, 6]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '72.43', 'commutator_count': 1, 'commutator_label': '36.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 402, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 3], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 3], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6720, 'exponent': 24, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '72.43', 'hash': 402, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 6, 2], 'inner_gens': [[1, 16, 264, 144], [17, 8, 240, 216], [193, 224, 24, 144], [1, 80, 24, 144]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_3:S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 16], [3, 8], [6, 4]], 'label': '288.402', 'linC_count': 72, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 6, 'linQ_dim': 7, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C12.S4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 36, 'number_divisions': 23, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 68, 'number_subgroups': 248, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 26], [4, 8], [6, 38], [8, 144], [12, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 8, 24, 144], [1, 16, 168, 144], [3, 112, 264, 144]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [3, 2], [4, 5], [6, 3], [12, 2]], 'representations': {'PC': {'code': 22675231374012014717598665098, 'gens': [1, 4, 5, 7], 'pres': [7, 2, 2, 2, 3, 2, 3, 2, 14, 36, 451, 9244, 1075, 102, 4037, 1350]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [11293, 140017, 24003, 72009, 60207, 130311, 540]}, 'Perm': {'d': 15, 'gens': [94447180922, 194123381760, 288369849600, 843, 1440, 7, 16]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.S_4', 'transitive_degree': 72, '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': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 8, 24, 144], [1, 8, 120, 144], [1, 16, 264, 144], [5, 8, 24, 144], [3, 8, 24, 144], [17, 8, 240, 216], [1, 104, 24, 144], [97, 8, 24, 144], [145, 224, 24, 144], [1, 80, 24, 144]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 72, 'aut_perms': [119104705619027829844289178024814194513020478876369172124638547721852809628426350200428029393631480, 6687643986850360475654769195338544889865432588698746975766707676481998180378565267642745007053430261, 8660026160654545993497270522209617247234983506768878788514676312025730343415543563822165298666347285781, 850828275212888371529444618539791166389365013336357835391274953932372908499614381585320177908853056816, 54362126952738340082700119758818943227791612403186596018643932385778641690507318750799517481762388994821, 4179761570608096679640365515766386688679288070613192003882467622360053352082839731583305361176904749, 20703151596379842745272631824867081493094904514533303865098858161807998727690135690723645150657655060576, 7786418879759582050403610847495620409648400786952607025511847971440210103549669995229765083468794493090, 6608255365820604288783102863724654969802626227039130111707139180693950712717615834214207398259609069], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 3, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 3, 1], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 8, 3], [4, 1, 2], [4, 3, 2], [6, 2, 1], [6, 6, 2], [6, 8, 3], [8, 18, 8], [12, 2, 2], [12, 6, 2], [12, 8, 6]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '72.43', 'commutator_count': 1, 'commutator_label': '36.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 402, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 3], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 3], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6720, 'exponent': 24, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '72.43', 'hash': 402, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 6, 2], 'inner_gens': [[1, 16, 264, 144], [17, 8, 240, 216], [193, 224, 24, 144], [1, 80, 24, 144]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_3:S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 16], [3, 8], [6, 4]], 'label': '288.402', 'linC_count': 72, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 6, 'linQ_dim': 7, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C12.S4', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 36, 'number_divisions': 23, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 68, 'number_subgroups': 248, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 26], [4, 8], [6, 38], [8, 144], [12, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 8, 24, 144], [1, 16, 168, 144], [3, 112, 264, 144]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [3, 2], [4, 5], [6, 3], [12, 2]], 'representations': {'PC': {'code': 22675231374012014717598665098, 'gens': [1, 4, 5, 7], 'pres': [7, 2, 2, 2, 3, 2, 3, 2, 14, 36, 451, 9244, 1075, 102, 4037, 1350]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [11293, 140017, 24003, 72009, 60207, 130311, 540]}, 'Perm': {'d': 15, 'gens': [94447180922, 194123381760, 288369849600, 843, 1440, 7, 16]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.S_4', 'transitive_degree': 72, '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}
