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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '1404.156', 'ambient_counter': 156, 'ambient_order': 1404, 'ambient_tex': 'C_3^2:D_{78}', 'central': False, 'central_factor': False, 'centralizer_order': 234, 'characteristic': False, 'core_order': 234, 'counter': 13, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1404.156.6.a1.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '6.a1.d1', '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '234.16', 'subgroup_hash': 16, 'subgroup_order': 234, 'subgroup_tex': 'C_3\\times C_{78}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1404.156', 'aut_centralizer_order': 234, 'aut_label': '6.a1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '144.159', 'aut_weyl_index': 936, 'centralizer': '6.a1.d1', 'complements': ['234.d1.e1', '234.d1.g1', '234.d1.f1', '234.d1.a1', '234.d1.c1', '234.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1', '3.a1.d1'], 'contains': ['12.a1.d1', '18.a1.a1', '18.b1.d1', '78.a1.d1'], 'core': '6.a1.d1', 'coset_action_label': None, 'count': 1, 'diagramx': [3766, 6031, 4719, 7277, 5386, 8702, 3512, 3396], 'generators': [702, 6, 108, 2], 'label': '1404.156.6.a1.d1', 'mobius_quo': 0, 'mobius_sub': 3, 'normal_closure': '6.a1.d1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['12.a1.d1', '18.a1.a1', '78.a1.d1'], 'normalizer': '1.a1.a1', 'old_label': '6.a1.d1', 'projective_image': '234.15', 'quotient_action_image': '6.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '6.a1.d1', 'subgroup_fusion': None, 'weyl_group': '6.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '234.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 12, 4, 12], 'aut_gens': [[1, 3], [2, 3], [157, 93], [79, 161], [78, 10]], 'aut_group': '576.5460', 'aut_hash': 5460, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 576, 'aut_permdeg': 15, 'aut_perms': [6314112000, 19766074464, 288518993280, 124711372803], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 8, 1], [6, 1, 8, 1], [13, 1, 12, 1], [26, 1, 12, 1], [39, 1, 96, 1], [78, 1, 96, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{12}\\times \\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '576.5460', 'autcent_hash': 5460, 'autcent_nilpotent': False, 'autcent_order': 576, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_{12}\\times \\GL(2,3)', '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, 1], [3, 1, 8], [6, 1, 8], [13, 1, 12], [26, 1, 12], [39, 1, 96], [78, 1, 96]], 'center_label': '234.16', 'center_order': 234, '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', '3.1', '3.1', '13.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 16, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['13.1', 1], ['2.1', 1], ['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 4], [6, 1, 2, 4], [13, 1, 12, 1], [26, 1, 12, 1], [39, 1, 24, 4], [78, 1, 24, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 42, 'exponent': 78, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 13], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '234.16', 'hash': 16, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 234]], 'label': '234.16', 'linC_count': 12096, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 42, 'linQ_dim': 16, 'linQ_dim_count': 42, 'linR_count': 3024, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3*C78', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 234, 'number_divisions': 20, 'number_normal_subgroups': 24, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 24, 'number_subgroups': 24, 'old_label': None, 'order': 234, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 1], [3, 8], [6, 8], [13, 12], [26, 12], [39, 96], [78, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 12, 4, 12], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[2, 3], [157, 93], [79, 161], [78, 10]], 'outer_group': '576.5460', 'outer_hash': 5460, 'outer_nilpotent': False, 'outer_order': 576, 'outer_permdeg': 15, 'outer_perms': [6314112000, 19766074464, 288518993280, 124711372803], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_{12}\\times \\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3, 13], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 8], [12, 2], [24, 8]], 'representations': {'PC': {'code': 2622483671, 'gens': [1, 2], 'pres': [4, -3, -2, -3, -13, 21, 46]}, 'GLFp': {'d': 2, 'p': 79, 'gens': [10846912, 27117168]}, 'Perm': {'d': 21, 'gens': [2432902008176640000, 12804747411456000, 2615348736000, 5748019200]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 78], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3\\times C_{78}', 'transitive_degree': 234, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 312, 'aut_gen_orders': [78, 24, 12, 12], 'aut_gens': [[1, 2, 6, 18], [1355, 942, 6, 34], [477, 948, 12, 1070], [107, 950, 6, 564], [647, 942, 6, 562]], 'aut_group': None, 'aut_hash': 1438572783930339138, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 134784, 'aut_permdeg': 234, 'aut_perms': [20775326010975616971656442483873950437829452754232578027676015246773330919497271604952592746098886390841591918472979596357608059440057152230104883054259619215081283998117261388470332369521689183719545101138354508514341654110138411322457978717889762259277766202707070120634785035043862704657150574633340940077784249387651044879634043526793145995975584032297670980608743111280270614699236324575657439166274681158278812189331356345735382910891195520254816073, 10565801552299234296963068359353256892953891302297779191910352258918759396794036111150032364281168354733187320813808055918751532196084939214316345614747880465536601770624021753832712356594095920775917420393345766829517242176409868934716052544210670008721793518378716378101686596355955947959688258372693187213810269961924267167028964238575271745529955396190924563960343036210048648061824490157259565435697966242194024565853831505344886391086496376848369586, 459321526184712271788481126099641713402097772451539831401415596914667245962708520637998621502811683729448430863298196942552476736828763159279788856292450009542634975555340287797297563678725445463768940764141436179232621697246248101273731391060492698680185035954692184036981353674054845693819638367119003072393227712915513282390646999282561756647283144532257681427919169385702426752891908202554230733101870671466176545253740624969871199855171364759153689, 9151682160636280339257871325259541306103243476249722173685131267972549061961484405929935650856517129905822453788141752654237300254351251139632333728482463636402072214691511967064083853218328982017466949388758426238487869092693332623039470135287314293237842325013717531747300943077428269265017153684011050613706948915149545894622601506762239986489816045787140341067459788469703339367219471441721833742440879397027968130231284054673613938884357983222392773], 'aut_phi_ratio': 312.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 117, 2, 1], [3, 1, 2, 1], [3, 6, 4, 1], [6, 1, 2, 1], [6, 6, 4, 1], [6, 117, 4, 1], [13, 2, 6, 1], [26, 2, 6, 1], [39, 2, 12, 1], [39, 6, 48, 1], [78, 2, 12, 1], [78, 6, 48, 1]], 'aut_supersolvable': False, 'aut_tex': '\\PSU(3,2).C_{39}.C_6.C_2^3', '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': 312, 'autcentquo_group': '67392.c', 'autcentquo_hash': 1849751742543539073, 'autcentquo_nilpotent': False, 'autcentquo_order': 67392, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{13}\\times C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 117, 2], [3, 1, 2], [3, 6, 4], [6, 1, 2], [6, 6, 4], [6, 117, 4], [13, 2, 6], [26, 2, 6], [39, 2, 12], [39, 6, 48], [78, 2, 12], [78, 6, 48]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '234.15', 'commutator_count': 2, 'commutator_label': '351.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '13.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 156, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['702.43', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 117, 1, 2], [3, 1, 2, 1], [3, 6, 1, 4], [6, 1, 2, 1], [6, 6, 1, 4], [6, 117, 2, 2], [13, 2, 6, 1], [26, 2, 6, 1], [39, 2, 12, 1], [39, 6, 12, 4], [78, 2, 12, 1], [78, 6, 12, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 7938, 'exponent': 78, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 3, 13], 'faithful_reps': [[6, 0, 12]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '468.54', 'hash': 156, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 78, 'inner_gen_orders': [2, 3, 1, 39], 'inner_gens': [[1, 4, 6, 1386], [5, 2, 6, 24], [1, 2, 6, 18], [37, 14, 6, 18]], 'inner_hash': 15, 'inner_nilpotent': False, 'inner_order': 234, 'inner_split': False, 'inner_tex': 'C_3:D_{39}', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 72, 'irrQ_dim': 72, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 116], [3, 8], [6, 24]], 'label': '1404.156', 'linC_count': 648, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 6, 'linQ_dim': 18, 'linQ_dim_count': 6, 'linR_count': 324, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:D78', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 14, 'number_characteristic_subgroups': 13, 'number_conjugacy_classes': 152, 'number_divisions': 28, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 40, 'number_subgroup_classes': 110, 'number_subgroups': 1882, 'old_label': None, 'order': 1404, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 235], [3, 26], [6, 494], [13, 12], [26, 12], [39, 312], [78, 312]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [6, 6, 4, 2, 4], 'outer_gen_pows': [0, 0, 0, 1, 0], 'outer_gens': [[5, 4, 12, 888], [707, 4, 6, 956], [1, 484, 6, 28], [1, 484, 6, 1324], [1, 946, 6, 32]], 'outer_group': '576.8445', 'outer_hash': 8445, 'outer_nilpotent': False, 'outer_order': 576, 'outer_permdeg': 21, 'outer_perms': [7810979630948887710, 15470002595199761281, 18058808507068183680, 30101295610529982720, 35837886365129439360], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times \\GL(2,3):C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [6, 4], [12, 2], [24, 8], [72, 2]], 'representations': {'PC': {'code': 5254560463577582430979028531620599767, 'gens': [1, 2, 3, 4], 'pres': [6, 2, 3, 3, 2, 3, 13, 49, 33267, 297, 69, 41044, 730, 118, 46661]}, 'Perm': {'d': 24, 'gens': [3581250984086188457647, 1, 29486791567144783872000, 54161398976798969856000, 99712902486, 82215563705523376128000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:D_{78}', 'transitive_degree': 234, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '2.1', '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, 4], [1, 3], [2, 4]], '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, 3, 1, 1], [3, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 3, 1], [3, 2, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 2, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 3, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.1', 'hash': 1, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3], 'inner_gens': [[1, 3], [2, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 2], [2, 1]], 'label': '6.1', 'linC_count': 1, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'S3', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 3, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 6, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 3], [3, 2]], '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': 2, 'perfect': False, 'permutation_degree': 3, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 25, 'gens': [1, 2], 'pres': [2, -2, -3, 17]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [28, 45]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'GL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'SL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGL'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'SO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'SU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PSO'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'PSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'GO'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'Omega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'PGO'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'POmega'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CSO'}, {'d': 2, 'q': 4, 'gens': [20, 194], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'CSOMinus'}, {'d': 2, 'q': 2, 'gens': [20, 69], 'family': 'CSU'}, {'d': 3, 'q': 2, 'gens': [84, 279], 'family': 'CO'}, {'d': 2, 'q': 2, 'gens': [13, 14], 'family': 'COMinus'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PGammaL'}, {'d': 2, 'q': 2, 'gens': [6, 11], 'family': 'PSigmaL'}, {'d': 2, 'q': 2, 'gens': [20, 138], 'family': 'PGammaU'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGL'}, {'d': 1, 'q': 3, 'gens': [1, 3], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11, 6]}, 'Perm': {'d': 3, 'gens': [1, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'S_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
