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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '21600.bg', 'ambient_counter': 33, 'ambient_order': 21600, 'ambient_tex': 'C_5\\times A_4\\times A_6', 'central': False, 'central_factor': True, 'centralizer_order': 60, 'characteristic': True, 'core_order': 1800, 'counter': 9, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '21600.bg.12.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '12.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '12.3', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 12, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4', 'simple': False, 'solvable': False, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '1800.555', 'subgroup_hash': 555, 'subgroup_order': 1800, 'subgroup_tex': 'C_5\\times A_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '21600.bg', 'aut_centralizer_order': None, 'aut_label': '12.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '360.a1.a1', 'complements': ['1800.a1.a1', '1800.e1.a1', '1800.j1.a1', '1800.e1.b1', '1800.j1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1.a1', '6.a1.a1'], 'contains': ['60.a1.a1', '72.b1.a1', '72.b1.b1', '120.g1.a1', '180.h1.a1', '180.h1.b1'], 'core': '12.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2965, 1297, 1502, 7968, 7717, 1084, 2603, 1081], 'generators': [10891566, 8431920, 4072925], 'label': '21600.bg.12.a1.a1', 'mobius_quo': 1, 'mobius_sub': 4, 'normal_closure': '12.a1.a1', 'normal_contained_in': ['3.a1.a1'], 'normal_contains': ['60.a1.a1', '4320.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '12.a1.a1', 'projective_image': '4320.bh', 'quotient_action_image': '1.1', 'quotient_action_kernel': '12.3', 'quotient_action_kernel_order': 12, 'quotient_fusion': None, 'short_label': '12.a1.a1', 'subgroup_fusion': None, 'weyl_group': '360.118'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 120, 'aut_gen_orders': [20, 4, 8], 'aut_gens': [[7711957, 19716532], [7712032, 15282093], [18628653, 8109472], [5120733, 8830912]], 'aut_group': '5760.db', 'aut_hash': 4554243923608446656, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5760, 'aut_permdeg': 49, 'aut_perms': [12678062723383880260666962986593826593262917772756076910732560, 37241750549754465475147654256289671377845487203652359038255279, 37241765880133789887432498463655847608990855804023233765231198], 'aut_phi_ratio': 12.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 45, 1, 1], [3, 40, 2, 1], [4, 90, 1, 1], [5, 1, 4, 1], [5, 72, 2, 1], [5, 72, 8, 1], [10, 45, 4, 1], [15, 40, 8, 1], [20, 90, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times S_6:C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '1440.5841', 'autcentquo_hash': 5841, 'autcentquo_nilpotent': False, 'autcentquo_order': 1440, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_6:C_2', 'cc_stats': [[1, 1, 1], [2, 45, 1], [3, 40, 2], [4, 90, 1], [5, 1, 4], [5, 72, 10], [10, 45, 4], [15, 40, 8], [20, 90, 4]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '360.118', 'commutator_count': 1, 'commutator_label': '360.118', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['5.1', '360.118'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 555, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['360.118', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 45, 1, 1], [3, 40, 1, 2], [4, 90, 1, 1], [5, 1, 4, 1], [5, 72, 2, 1], [5, 72, 4, 2], [10, 45, 4, 1], [15, 40, 4, 2], [20, 90, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 318, 'exponent': 60, 'exponents_of_order': [3, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[5, 0, 8], [8, 0, 8], [9, 0, 4], [10, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1800.555', 'hash': 555, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [5, 4], 'inner_gens': [[7711957, 15604612], [7379317, 19716532]], 'inner_hash': 118, 'inner_nilpotent': False, 'inner_order': 360, 'inner_split': False, 'inner_tex': 'A_6', 'inner_used': [1, 2], 'irrC_degree': 5, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 10, 'irrep_stats': [[1, 5], [5, 10], [8, 10], [9, 5], [10, 5]], 'label': '1800.555', 'linC_count': 8, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 2, 'linQ_dim': 9, 'linQ_dim_count': 2, 'linR_count': 4, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C5*A6', 'ngens': 2, '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 35, 'number_divisions': 13, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 33, 'number_subgroup_classes': 46, 'number_subgroups': 1146, 'old_label': None, 'order': 1800, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 45], [3, 80], [4, 90], [5, 724], [10, 180], [15, 320], [20, 360]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4], 'outer_gen_pows': [8760352, 12468997, 0], 'outer_gens': [[4365397, 15604612], [16047397, 16012132], [7712032, 19716573]], 'outer_group': '16.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [5, 2], [9, 1], [10, 1], [16, 1], [20, 2], [32, 2], [36, 1], [40, 1]], 'representations': {'Perm': {'d': 11, 'gens': [7711957, 19716532]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [5], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times A_6', 'transitive_degree': 30, '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': '15.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 120, 'aut_gen_orders': [30, 6, 24, 6, 6], 'aut_gens': [[87657292800, 274467916800, 100111334400, 12454041936, 12454041626, 100122225840], [186810624000, 87657292800, 267761894400, 262013875805, 262013875614, 267765966720], [274467916800, 186810624000, 267761894400, 12454041856, 12454042247, 267772785840], [274467916800, 186810624000, 6706022400, 181062605284, 181062604826, 6714454320], [274467916800, 87657292800, 12454041600, 100111334862, 100111334534, 12464933040], [186810624000, 87657292800, 267761894400, 262013875891, 262013875913, 267772785840]], 'aut_group': None, 'aut_hash': 3276841175708577286, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 138240, 'aut_permdeg': 57, 'aut_perms': [28864642645510784913822712568338074894966545558538332801404185879885243627209, 406754175148224496264176332651967572413958800451502465252211691197479430041, 24970002017494506648920163229180824837034396418307601982675276446746129142256, 7083116372180273981603048098034343163928645393911102376583004552491652171634, 36569130611034786872933803060699834655504437890301521749663823280208361801470], 'aut_phi_ratio': 24.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 45, 1, 1], [2, 135, 1, 1], [3, 4, 2, 1], [3, 40, 2, 1], [3, 160, 4, 1], [4, 90, 1, 1], [4, 270, 1, 1], [5, 1, 4, 1], [5, 72, 2, 1], [5, 72, 8, 1], [6, 120, 2, 1], [6, 180, 2, 1], [10, 3, 4, 1], [10, 45, 4, 1], [10, 135, 4, 1], [10, 216, 2, 1], [10, 216, 8, 1], [12, 360, 2, 1], [15, 4, 8, 1], [15, 40, 8, 1], [15, 160, 16, 1], [15, 288, 4, 1], [15, 288, 16, 1], [20, 90, 4, 1], [20, 270, 4, 1], [30, 120, 8, 1], [30, 180, 8, 1], [60, 360, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times A_6.C_2^2\\times S_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '34560.m', 'autcentquo_hash': 7190829667096474948, 'autcentquo_nilpotent': False, 'autcentquo_order': 34560, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4\\times S_6:C_2', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 45, 1], [2, 135, 1], [3, 4, 2], [3, 40, 2], [3, 160, 4], [4, 90, 1], [4, 270, 1], [5, 1, 4], [5, 72, 10], [6, 120, 2], [6, 180, 2], [10, 3, 4], [10, 45, 4], [10, 135, 4], [10, 216, 10], [12, 360, 2], [15, 4, 8], [15, 40, 8], [15, 160, 16], [15, 288, 20], [20, 90, 4], [20, 270, 4], [30, 120, 8], [30, 180, 8], [60, 360, 8]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '4320.bh', 'commutator_count': 1, 'commutator_label': '1440.5845', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '360.118'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 33, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['12.3', 1], ['360.118', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 45, 1, 1], [2, 135, 1, 1], [3, 4, 2, 1], [3, 40, 1, 2], [3, 160, 2, 2], [4, 90, 1, 1], [4, 270, 1, 1], [5, 1, 4, 1], [5, 72, 2, 1], [5, 72, 4, 2], [6, 120, 1, 2], [6, 180, 2, 1], [10, 3, 4, 1], [10, 45, 4, 1], [10, 135, 4, 1], [10, 216, 2, 1], [10, 216, 4, 2], [12, 360, 2, 1], [15, 4, 8, 1], [15, 40, 4, 2], [15, 160, 8, 2], [15, 288, 4, 1], [15, 288, 8, 2], [20, 90, 4, 1], [20, 270, 4, 1], [30, 120, 4, 2], [30, 180, 8, 1], [60, 360, 8, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1272, 'exponent': 60, 'exponents_of_order': [5, 3, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[15, 0, 8], [24, 0, 8], [27, 0, 4], [30, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '21600.bg', 'hash': 1049615865346914016, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 3, 12, 6, 3], 'inner_gens': [[87657292800, 274467916800, 174356582400, 181062605136, 181062604826, 174367473840], [87657292800, 274467916800, 267761894400, 93405312336, 93405312026, 267772785840], [186810624000, 87657292800, 100111334400, 181062605136, 181062604826, 100122225840], [274467916800, 186810624000, 267761894400, 12454041936, 12454042287, 267772785840], [274467916800, 186810624000, 267761894400, 12454041742, 12454041626, 267772785840], [186810624000, 87657292800, 100111334400, 181062605136, 181062604826, 100122225840]], 'inner_hash': 8888903546687000962, 'inner_nilpotent': False, 'inner_order': 4320, 'inner_split': False, 'inner_tex': 'A_4\\times A_6', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 15, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': 30, 'irrep_stats': [[1, 15], [3, 5], [5, 30], [8, 30], [9, 15], [10, 15], [15, 10], [24, 10], [27, 5], [30, 5]], 'label': '21600.bg', 'linC_count': 144, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 12, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C5*A4*A6', '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, 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, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 30, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 140, 'number_divisions': 39, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 223, 'number_subgroup_classes': 322, 'number_subgroups': 22252, 'old_label': None, 'order': 21600, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 183], [3, 728], [4, 360], [5, 724], [6, 600], [10, 2892], [12, 720], [15, 8672], [20, 1440], [30, 2400], [60, 2880]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 352, 425, 0], 'outer_gens': [[186810624000, 274467916800, 262013875200, 174356582736, 174356582426, 262024766640], [87657292800, 274467916800, 100111334400, 12454041908, 12454041607, 100122225840], [87657292800, 274467916800, 100111334400, 12454042196, 12454042287, 100122225840], [87657292800, 274467916800, 100111334400, 12454041936, 12454041626, 100119766320]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [3, 1], [4, 1], [5, 2], [8, 1], [9, 1], [10, 3], [12, 1], [15, 2], [16, 1], [18, 1], [20, 3], [27, 1], [30, 1], [32, 3], [36, 1], [40, 3], [48, 1], [60, 2], [64, 2], [72, 1], [80, 1], [96, 2], [108, 1], [120, 1]], 'representations': {'Perm': {'d': 15, 'gens': [87657292800, 274467916800, 100111334400, 12454041936, 12454041626, 100122225840]}}, 'schur_multiplier': [2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [15], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times A_4\\times A_6', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 3, 2, 2], 'aut_gens': [[4, 16, 7], [11, 16, 23], [19, 23, 16], [8, 16, 7], [15, 16, 7]], 'aut_group': '24.12', 'aut_hash': 12, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 4, 'aut_perms': [2, 4, 16, 7], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 4, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_4', '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': 12, 'autcentquo_group': '24.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_4', 'cc_stats': [[1, 1, 1], [2, 3, 1], [3, 4, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '12.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [3, 4, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 4, 'exponent': 6, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[3, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '12.3', 'hash': 3, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 2, 2], 'inner_gens': [[4, 7, 23], [19, 16, 7], [15, 16, 7]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'A_4', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 3, 'irrQ_dim': 3, 'irrR_degree': 3, 'irrep_stats': [[1, 3], [3, 1]], 'label': '12.3', 'linC_count': 1, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 3, 'linQ_degree_count': 1, 'linQ_dim': 3, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'A4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 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': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 5, 'number_subgroup_classes': 5, 'number_subgroups': 10, 'old_label': None, 'order': 12, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [3, 8]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3, 7, 16]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 4, 'pgroup': 0, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [3, 1]], 'representations': {'PC': {'code': 9572, 'gens': [1, 2, 3], 'pres': [3, -3, -2, 2, 55, 29]}, 'GLZ': {'b': 3, 'd': 3, 'gens': [4828, 4708]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [31, 21], 'family': 'PSL'}, {'d': 2, 'q': 3, 'gens': [362, 766], 'family': 'PSU'}, {'d': 3, 'q': 3, 'gens': [10315, 1638], 'family': 'Omega'}, {'d': 3, 'q': 3, 'gens': [10315, 1638], 'family': 'POmega'}, {'d': 2, 'q': 3, 'gens': [31, 21], 'family': 'PSigmaL'}, {'d': 1, 'q': 4, 'gens': [3, 7], 'family': 'AGL'}], 'GLFp': {'d': 3, 'p': 2, 'gens': [458, 314, 124]}, 'Perm': {'d': 4, 'gens': [4, 16, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
