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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4400.j', 'ambient_counter': 10, 'ambient_order': 4400, 'ambient_tex': 'C_{44}:C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 1100, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4400.j.4.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1100.32', 'subgroup_hash': 32, 'subgroup_order': 1100, 'subgroup_tex': 'C_{110}:C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4400.j', 'aut_centralizer_order': 4, 'aut_label': '4.a1', 'aut_quo_index': 6, 'aut_stab_index': 2, 'aut_weyl_group': '4400.r', 'aut_weyl_index': 8, 'centralizer': '220.a1', 'complements': ['1100.f1'], 'conjugacy_class_count': 2, 'contained_in': ['2.a1', '2.b1', '2.c1'], 'contains': ['8.a1', '8.c1', '20.a1', '20.b1', '44.a1'], 'core': '4.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6185, 4576, 3644, 3920], 'generators': [50, 2, 20, 2200, 400], 'label': '4400.j.4.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.a1', 'normal_contained_in': ['2.a1', '2.b1', '2.c1'], 'normal_contains': ['8.a1', '20.a1', '20.b1'], 'normalizer': '1.a1', 'old_label': '4.a1', 'projective_image': '440.42', 'quotient_action_image': '2.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '4.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '100.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [20, 10, 20, 22], 'aut_gens': [[1, 10], [1041, 735], [51, 610], [756, 585], [256, 565]], 'aut_group': None, 'aut_hash': 8567286445053474119, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 13200, 'aut_permdeg': 58, 'aut_perms': [718230018297900493602370197653177412626078745796844305279817728679584925887367, 282454375993587955618354062051943574624879558108614483592707852075976998756633, 2203403494065038552380618279406710491936220411947943900168440217368203238437464, 358456208908161791723591364165440803806313767756036098529359424557000068289284], 'aut_phi_ratio': 33.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 12, 1], [10, 11, 15, 4], [11, 5, 2, 1], [22, 5, 6, 1], [55, 5, 8, 1], [110, 5, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{55}.C_{30}.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 60, 'autcent_group': '120.36', 'autcent_hash': 36, 'autcent_nilpotent': False, 'autcent_order': 120, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [5, 1, 4], [5, 11, 20], [10, 1, 12], [10, 11, 60], [11, 5, 2], [22, 5, 6], [55, 5, 8], [110, 5, 24]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '55.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '5.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 32, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1], ['55.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 3], [10, 11, 4, 15], [11, 5, 2, 1], [22, 5, 2, 3], [55, 5, 8, 1], [110, 5, 8, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 110, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1100.32', 'hash': 32, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 55, 'inner_gen_orders': [5, 11], 'inner_gens': [[1, 910], [201, 10]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 55, 'inner_split': True, 'inner_tex': 'C_{11}:C_5', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 100], [5, 40]], 'label': '1100.32', 'linC_count': 1440, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 30, 'linQ_dim': 14, 'linQ_dim_count': 30, 'linR_count': 24, 'linR_degree': 11, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C110:C10', 'ngens': 5, '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': 10, 'number_conjugacy_classes': 140, 'number_divisions': 36, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 80, 'number_subgroups': 380, 'old_label': None, 'order': 1100, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 3], [5, 224], [10, 672], [11, 10], [22, 30], [55, 40], [110, 120]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 4, 30], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[551, 210], [771, 230], [771, 1065]], 'outer_group': '240.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 240, 'outer_permdeg': 10, 'outer_perms': [6, 81367, 816511], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6\\times F_5', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 24], [10, 4], [40, 4]], 'representations': {'PC': {'code': 28115612631882597466476069066903039, 'gens': [1, 3], 'pres': [5, -2, -5, -2, -5, -11, 10, 13652, 2332, 42, 14403, 6208, 118, 7504, 11259]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [1094552356, 836204792, 857494092, 1714988184, 427330445]}, 'Perm': {'d': 20, 'gens': [7, 16, 7180459198260600, 46200, 135543344769504000]}}, 'schur_multiplier': [10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10, 10], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{110}:C_{10}', 'transitive_degree': 220, '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': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 20, 20, 20, 10], 'aut_gens': [[1, 10, 100], [2583, 756, 300], [1501, 3574, 300], [4165, 3774, 4100], [1, 1838, 2500], [101, 1938, 1500], [1601, 2610, 3100]], 'aut_group': None, 'aut_hash': 2437826575940019868, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 35200, 'aut_permdeg': 81, 'aut_perms': [4555388998179032647089305550864848335304769513432943178265188568622987650625154040138747736440211584547246988808352492955, 3020275665081616031422391807499702152788409405642771204441617566138958051699474777274271653767785642036586948012823366147, 678615547409289874301823831385976391706417033364048070217212857434801433985228892083822953000902987656219551668994150335, 5496778742352979675825693466198549807708382509728876385776560889902546603416618919712330836826510531825169096589037693984, 2527705418138644378424441807050802391714847636576206926482056116327465501024334099191350906123287611713887560887835566512, 3276114896137516766636654758155380959030296635384240992820167249871469644618553785722331608137995498427076016910649595491], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [2, 11, 2, 1], [2, 22, 2, 1], [4, 2, 1, 1], [4, 22, 1, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 4, 1], [10, 2, 8, 1], [10, 11, 5, 4], [10, 11, 8, 1], [10, 11, 10, 4], [10, 22, 8, 1], [10, 22, 10, 8], [11, 10, 1, 1], [20, 2, 4, 1], [20, 22, 4, 1], [20, 22, 5, 8], [22, 10, 1, 1], [22, 20, 2, 1], [44, 20, 1, 1], [55, 10, 4, 1], [110, 10, 4, 1], [110, 20, 8, 1], [220, 20, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{110}.C_{10}.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.236', 'autcent_hash': 236, 'autcent_nilpotent': False, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '220.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 220, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [2, 11, 2], [2, 22, 2], [4, 2, 1], [4, 22, 1], [5, 1, 4], [5, 11, 20], [10, 1, 4], [10, 2, 8], [10, 11, 68], [10, 22, 88], [11, 10, 1], [20, 2, 4], [20, 22, 44], [22, 10, 1], [22, 20, 2], [44, 20, 1], [55, 10, 4], [110, 10, 4], [110, 20, 8], [220, 20, 4]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '440.42', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['110.1', 1], ['5.1', 1], ['8.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [2, 11, 1, 2], [2, 22, 1, 2], [4, 2, 1, 1], [4, 22, 1, 1], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 1], [10, 2, 4, 2], [10, 11, 4, 17], [10, 22, 4, 22], [11, 10, 1, 1], [20, 2, 4, 1], [20, 22, 4, 11], [22, 10, 1, 1], [22, 20, 1, 2], [44, 20, 1, 1], [55, 10, 4, 1], [110, 10, 4, 1], [110, 20, 4, 2], [220, 20, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 749952, 'exponent': 220, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2200.a', 'hash': 532271021746972557, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 10, 22], 'inner_gens': [[1, 1610, 1900], [2801, 10, 300], [2601, 4210, 100]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 440, 'inner_split': True, 'inner_tex': 'C_2^2\\times F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 20, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 40, 'irrep_stats': [[1, 200], [2, 50], [10, 20], [20, 5]], 'label': '4400.j', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C44:C10^2', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 50, 'number_characteristic_subgroups': 35, 'number_conjugacy_classes': 275, 'number_divisions': 80, 'number_normal_subgroups': 164, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 432, 'number_subgroups': 3160, 'old_label': None, 'order': 4400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 71], [4, 24], [5, 224], [10, 2704], [11, 10], [20, 976], [22, 50], [44, 20], [55, 40], [110, 200], [220, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 10], 'outer_gen_pows': [0, 0, 1564], 'outer_gens': [[3801, 10, 2100], [2065, 2492, 2100], [3165, 2374, 2100]], 'outer_group': '80.50', 'outer_hash': 50, 'outer_nilpotent': False, 'outer_order': 80, 'outer_permdeg': 9, 'outer_perms': [7, 5896, 122543], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 48], [8, 12], [10, 4], [20, 1], [40, 4], [80, 1]], 'representations': {'PC': {'code': '18053028909108461072444892686717030496013806886236833688186436148639481314671890303009', 'gens': [1, 3, 5], 'pres': [7, -2, -5, -2, -5, -2, -2, -11, 14, 33812, 12714, 58, 56563, 5890, 66504, 15761, 1068, 1600, 102, 159605, 37812, 2539, 3806, 124, 156806, 88213, 5900, 8847]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 31471887339564514, 10885681761182519, 10522401710269773, 19623198237756269, 33418192856010432, 11184584018506052]}, 'Perm': {'d': 20, 'gens': [34, 13606353239673671, 142700251934419991, 244009609488732240, 41074, 271082647280885113, 33455996122389911]}}, 'schur_multiplier': [2, 2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{44}:C_{10}^2', 'transitive_degree': 220, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
