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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.18221', 'ambient_counter': 18221, 'ambient_order': 384, 'ambient_tex': 'C_2^5:A_4', 'central': False, 'central_factor': False, 'centralizer_order': 32, 'characteristic': True, 'core_order': 32, 'counter': 14, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.18221.12.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '12.a1', 'outer_equivalence': True, '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': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '32.51', 'subgroup_hash': 51, 'subgroup_order': 32, 'subgroup_tex': 'C_2^5', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.18221', 'aut_centralizer_order': 256, 'aut_label': '12.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '288.1026', 'aut_weyl_index': 256, 'centralizer': '12.a1', 'complements': ['32.c1'], 'conjugacy_class_count': 1, 'contained_in': ['4.a1', '6.d1'], 'contains': ['24.a1', '24.g1', '24.i1', '24.k1'], 'core': '12.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5445, 748, 4189, 4308], 'generators': [41868120, 101693640, 135359423, 178981920, 178981936], 'label': '384.18221.12.a1', 'mobius_quo': 0, 'mobius_sub': 4, 'normal_closure': '12.a1', 'normal_contained_in': ['3.a1'], 'normal_contains': ['24.a1', '48.a1'], 'normalizer': '1.a1', 'old_label': '12.a1', 'projective_image': '384.18221', 'quotient_action_image': '12.3', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '12.a1', 'subgroup_fusion': None, 'weyl_group': '12.3'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 26040, 'aut_gen_orders': [2, 5], 'aut_gens': [[1, 2, 4, 8, 16], [5, 2, 4, 12, 16], [11, 8, 27, 26, 13]], 'aut_group': '9999360.a', 'aut_hash': 2505043529366670169, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9999360, 'aut_permdeg': 31, 'aut_perms': [2450617681096434660778009755366, 945758899833610526331495647332850], 'aut_phi_ratio': 624960.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 31, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(5,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 26040, 'autcent_group': '9999360.a', 'autcent_hash': 2505043529366670169, 'autcent_nilpotent': False, 'autcent_order': 9999360, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(5,2)', '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, 31]], 'center_label': '32.51', 'center_order': 32, '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'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 51, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 5]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 31]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3, 5, 7, 31], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '32.51', 'hash': 51, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 16], [1, 2, 4, 8, 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, 32]], 'label': '32.51', 'linC_count': None, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, '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': 'C2^5', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 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': 32, 'number_divisions': 32, 'number_normal_subgroups': 374, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 374, 'number_subgroups': 374, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 31]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 26040, 'outer_gen_orders': [2, 5], 'outer_gen_pows': [0, 0], 'outer_gens': [[5, 2, 4, 12, 16], [11, 8, 27, 26, 13]], 'outer_group': '9999360.a', 'outer_hash': 2505043529366670169, 'outer_nilpotent': False, 'outer_order': 9999360, 'outer_permdeg': 31, 'outer_perms': [2450617681096434660778009755366, 945758899833610526331495647332850], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(5,2)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 32]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3, 4, 5], 'pres': [5, -2, 2, 2, 2, 2]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 705686952884, 706461793860, 706460730980, 706461792404]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [5226561, 7292993, 5128257, 20225089, 6210625]}, 'Perm': {'d': 10, 'gens': [362880, 5040, 120, 6, 1]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5', 'transitive_degree': 32, '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': '6.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 3, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 8], 'aut_gens': [[41868120, 727204, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 142618440, 175351807, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 138989520, 182610856, 135359416, 135359423, 101693640, 135359400], [41868120, 102337324, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 135072724, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [287216040, 15649924, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [211977360, 95080339, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [211977360, 19278844, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 177897728, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 94434607, 138989527, 101693663, 101693647, 178981920, 101693640], [41868120, 727204, 18553680, 22182607, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 94434607, 138989543, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 142618440, 138989527, 7, 178981936, 178981920, 101693640], [41868120, 404043, 142618463, 124104967, 101693663, 16, 178981920, 135359400]], 'aut_group': None, 'aut_hash': 970489985340270929, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 73728, 'aut_permdeg': 128, 'aut_perms': [358541790965542093444371689153042067284567802378112229744254395296851226747003800042818227412799840409058082563564023403027357809568837928860363596973848629513172069529920974234133796446125330598960018449654919393369, 6175840722114296862329573274787239314282994007507622531930745656928815267373801492942991056770893085144469932909470980549725879287457590949771873311793049198668410965762478236516975582798210371935758327207404525995, 318215115092909233955103372585277611506972317558536502889526536233178089932803533917050867393190391883286142834457724455122074334487404322212023100206242756620467859889961248728914307450950772614793685849708821878699, 98949571366223382255378136245851477616928310746190309662383964557266530208360216429789217261881703648039849176482989563133532707544217480271636252200726925178985069306621261001173773351180985053407430337732815965979, 79510847018868441080488372270465721992588820200527977306869124645145882066536498484261775095644889421714051027988428756540194979896935621775160812023221257338442684244359463708292178684695613195953927873381002925114, 250501359474105673919037336373969193827790825327698913996366879589819441923217701224602607269688025788507638904475134739771697453311265809705772711237025097699230022010363749139050829211915488530289101014989225699513, 183347320971409948920289827998893041604145852179150247149537214436701678439887226378010124076950436888720650632994122228653819689295011118676963611826101827428748352564067121072224866860610053048857697504792495659489, 58081560677119571816779894231328215752950782887494305633583212866663401000623245460545310429898502650732104600068244317612727995143552253445755409224125878873679449725767065415075369762885881828049113931633952043742, 308581366365449800849661653845091448458604827016223688755340754246632555873492878375677743445072013866210834925206594698050938792083616166459690105408012000953283179084554983549269340615563079231287198035537134960, 316359361511549575313643638653968424916898792902032847951338818287910148779940732604073193304741979549769893976494377159577877653547824462438675549426769506695010352817990692122403204170927947467300229533138358091585, 84383080239339467982072869040813475973814497607661977972285003091541448723086258971338026616055121966359288666849810588618673552779684015857873475085244858760200701188540128349037401499796923372071507961904580330084, 522075453929014841407559419618418310237410869844290304944736778638322326317894469236779443347702235655470639750880966252537174596573258660051618777104253006512485505762007511333226199714033752535442520594191675174, 175711415695782466096995346693681038098269346784437430160606178630110110371748507470858335552670911832152243304820560683772849662380236140065580587736503573724123520804334342771321203679206856367278466786437953131267], 'aut_phi_ratio': 576.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 3, 4, 1], [2, 4, 1, 1], [2, 6, 8, 1], [2, 12, 1, 1], [3, 64, 2, 1], [4, 12, 4, 1], [6, 64, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.C_2^6.C_3.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': 24, 'autcentquo_group': None, 'autcentquo_hash': 970489985340270929, 'autcentquo_nilpotent': False, 'autcentquo_order': 73728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6.C_2^6.C_3.S_3', 'cc_stats': [[1, 1, 1], [2, 3, 5], [2, 4, 1], [2, 6, 8], [2, 12, 1], [3, 64, 2], [4, 12, 4], [6, 64, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '384.18221', 'commutator_count': 1, 'commutator_label': '64.267', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 18221, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 5], [2, 4, 1, 1], [2, 6, 1, 8], [2, 12, 1, 1], [3, 64, 2, 1], [4, 12, 1, 4], [6, 64, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 455, 'exponent': 12, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '96.229', 'hash': 18221, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 2, 2, 2, 2, 2, 2], 'inner_gens': [[41868120, 727204, 142618440, 175351807, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 182610840, 94434623, 178981943, 178981927, 135359400, 178981920], [255634560, 138701644, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [287216040, 181525815, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 135072735, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 135072739, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 102337324, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640], [41868120, 135072724, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640]], 'inner_hash': 18221, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': False, 'inner_tex': 'C_2^5:A_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 6], [3, 10], [6, 8]], 'label': '384.18221', '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': 'C2^5:A4', 'ngens': 8, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 24, 'number_divisions': 22, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 824, 'number_subgroups': 4726, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 79], [3, 128], [4, 48], [6, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [41868120, 41868120, 0, 0, 41868120, 41868120, 0], 'outer_gens': [[41868120, 404043, 18553696, 14923576, 135359423, 135359416, 178981920, 135359400], [41868120, 727204, 164062103, 22182623, 16, 178981943, 178981920, 101693640], [41868120, 727204, 164062103, 83502720, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 18553687, 22182623, 101693647, 101693656, 178981920, 101693640], [41868120, 727204, 142618447, 22182623, 135359407, 16, 178981920, 101693640], [41868120, 727204, 164062103, 22182600, 7, 178981936, 178981920, 101693640], [41868120, 727204, 18553680, 22182607, 101693647, 101693656, 178981920, 101693640]], 'outer_group': '192.1493', 'outer_hash': 1493, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 8, 'outer_perms': [5183, 680, 19342, 26815, 94, 403, 5490], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^3:S_4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [3, 10], [6, 8]], 'representations': {'PC': {'code': 271502236956114684852021134833704395316592960, 'gens': [1, 3, 4, 5, 6, 7, 8], 'pres': [8, -2, -3, -2, 2, -2, 2, -2, 2, 16, 4898, 2530, 3651, 1643, 2884, 4812, 10373, 8653, 10758, 8078, 18439, 3087]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [11762753, 17076961, 5522529, 32746561, 5128257, 17076289, 5521524, 6210625]}, 'Perm': {'d': 12, 'gens': [41868120, 727204, 94434600, 138989527, 101693647, 101693656, 178981920, 101693640]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:A_4', 'transitive_degree': 24, '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}
