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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '87780.b', 'ambient_counter': 2, 'ambient_order': 87780, 'ambient_tex': 'C_{209}\\times D_{210}', 'central': False, 'central_factor': False, 'centralizer_order': 418, 'characteristic': False, 'core_order': 770, 'counter': 41, 'cyclic': False, 'direct': None, 'hall': 770, 'label': '87780.b.57.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '57.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 57, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1540.34', 'subgroup_hash': 34, 'subgroup_order': 1540, 'subgroup_tex': 'C_{11}\\times D_{70}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '87780.b', 'aut_centralizer_order': None, 'aut_label': '57.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.a1.a1', '19.a1.a1'], 'contains': ['114.a1.a1', '114.b1.a1', '114.b1.b1', '285.a1.a1', '399.a1.a1', '627.a1.a1'], 'core': '114.a1.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [9026, -1, 1077, -1, 5044, -1, 979, -1], 'generators': [1, 55860, 35112, 43890, 75240], 'label': '87780.b.57.a1.a1', 'mobius_quo': None, 'mobius_sub': 1, 'normal_closure': '19.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.a1.a1', 'old_label': '57.a1.a1', 'projective_image': '3990.19', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '57.a1.a1', 'subgroup_fusion': None, 'weyl_group': '70.3'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '44.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [60, 12, 60, 12, 30], 'aut_gens': [[1, 2], [529, 206], [441, 794], [155, 494], [1189, 1054], [89, 822]], 'aut_group': None, 'aut_hash': 6681869362728804958, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16800, 'aut_permdeg': 80, 'aut_perms': [70956726055744868681877619304417505562304607922636457676264554652759046639706188599637728059698208245843193255148036314, 28263376922616213042484429226673739480931975562189922737696008717997505549987006814220557269445503537014473729749205245, 33793946703555957851481724480338301488453137885140663171067117971751037000149079548505746567726070501984731830517884875, 64571473644106269196332132280971994465187915610556272691455255325863542141681986639723001754581541329816898612759139828, 48445380145407329562695410396757320093404955292180277965764431163847755186852619425619748211951062210352216736114817585], 'aut_phi_ratio': 35.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 35, 2, 1], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [22, 1, 10, 1], [22, 35, 20, 1], [35, 2, 12, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [154, 2, 30, 1], [385, 2, 120, 1], [770, 2, 120, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{10}\\times F_5\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '20.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 20, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '840.139', 'autcentquo_hash': 139, 'autcentquo_nilpotent': False, 'autcentquo_order': 840, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 35, 2], [5, 2, 2], [7, 2, 3], [10, 2, 2], [11, 1, 10], [14, 2, 3], [22, 1, 10], [22, 35, 20], [35, 2, 12], [55, 2, 20], [70, 2, 12], [77, 2, 30], [110, 2, 20], [154, 2, 30], [385, 2, 120], [770, 2, 120]], 'center_label': '22.2', 'center_order': 22, 'central_product': True, 'central_quotient': '70.3', 'commutator_count': 1, 'commutator_label': '35.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '7.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 34, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1], ['70.3', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 35, 1, 2], [5, 2, 2, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [22, 1, 10, 1], [22, 35, 10, 2], [35, 2, 12, 1], [55, 2, 20, 1], [70, 2, 12, 1], [77, 2, 30, 1], [110, 2, 20, 1], [154, 2, 30, 1], [385, 2, 120, 1], [770, 2, 120, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 770, 'exponents_of_order': [2, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 5, 7, 11], 'faithful_reps': [[2, 0, 120]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1540.34', 'hash': 34, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 70, 'inner_gen_orders': [2, 35], 'inner_gens': [[1, 838], [705, 2]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 70, 'inner_split': True, 'inner_tex': 'D_{35}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': 4, 'irrep_stats': [[1, 44], [2, 374]], 'label': '1540.34', 'linC_count': 120, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 14, 'linQ_dim': 20, 'linQ_dim_count': 14, 'linR_count': 420, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C11*D70', '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, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 418, 'number_divisions': 20, 'number_normal_subgroups': 22, 'number_subgroup_autclasses': 32, 'number_subgroup_classes': 40, 'number_subgroups': 304, 'old_label': None, 'order': 1540, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 71], [5, 4], [7, 6], [10, 4], [11, 10], [14, 6], [22, 710], [35, 24], [55, 40], [70, 24], [77, 60], [110, 40], [154, 60], [385, 240], [770, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 2, 60], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[771, 702], [1, 702], [1, 346]], 'outer_group': '240.185', 'outer_hash': 185, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [1307674368000, 6314112000, 43914273], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_{60}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 2], [6, 2], [10, 4], [24, 2], [40, 2], [60, 2], [240, 2]], 'representations': {'PC': {'code': 840028496790101388505400359, 'gens': [1, 2], 'pres': [5, -2, -2, -5, -7, -11, 8381, 26, 2042, 87, 13603, 158]}, 'GLFp': {'d': 2, 'p': 419, 'gens': [30748104663, 30292984759]}, 'Perm': {'d': 25, 'gens': [25903229347167063091200, 1, 522956310, 397620186163200, 672254738740453220352000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 22], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\times D_{70}', 'transitive_degree': 770, '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': '836.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 1260, 'aut_gen_orders': [30, 30, 90, 18, 36, 36, 180], 'aut_gens': [[1, 2], [10033, 782], [81929, 60862], [4599, 45862], [8361, 17818], [86945, 43426], [63119, 68066], [65627, 63746]], 'aut_group': None, 'aut_hash': 2033270074591517444, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1814400, 'aut_permdeg': 238, 'aut_perms': [69778355189459708007787394956610462443561028878046385800162611408871682115663417485569241297240395215374706387778861274836564426489465134031801107114822089376497682832109596729430148019494676541736061702503836477437118012651745752111252986082688277895862234858102127727579253123928580806390362031949732119173432731285669990097026460797769323574750306888819450761493430493779577267678416880572466901097297012121099280707004245824820548502933856341879380836944882076, 1925527012032712731748275232398355219139824113979208300848243777039907833696335045383180016192166272585442909277693021562626762956656765699327319967366026914019902856804139895126172147061151631243458835347426952200475699672327287129477767973116247976616954854333017475918326112328738941327410270607701731343838236562337458316727113609753251323793111975964578007343689148174816507502580796671594630445320576146471413317908181006069602446848128929920574506008802957, 46800512424941050524139015936764027066703040832578968924988571149648503254238814508736786963844456418658745124856562140015630300604088524592209718418863725002622248067302649986780249146972900396282887874521074030622005870536693092717463725908297491199770188770607270690235443711139053661940444604769826859781767551280812563828177484084631316404480330097859725631338729326345798822059522898953246408309472025182569993409476264994090430024149132879322200689920387440, 65572903391678349078334863083690246279945489032263007980785363567477965841737155018557761269171078893761898948035800899536836470325744978531575186940995412203112042036289146612700284558849291726782954112960576871212801623420978604599010468146062360696606998461586126252750357370896917855716917720922733896650364924138986477040947435984986137135791766206994756231169946986370794319992757364051665389333450251831394053786130035308949332945820095517753275936403772278, 57930182229016295023773524490090483823543586085299170739665129712945327007680745487736773391691692332315250930725889629238357921735189025121369732710232252618530632479898758829891619409205530558555806495608397324163208069411902911014279044405383881799098278221630024515333155467722746799320883561177108087464162371458170232780170601444328553447589887982940559527180712982986150799504323814683134289537870075307043481169031550840670328689932296203124642100706217646, 19950431848282371196759436103919363498644983175888556395349302478911268741431441969727264771060932310595300358378773670705103533690905635614731087265695128148210181966097532329481643945701873461375888205189371951562455485699914823806182355995310516927881706372832709005717863115819158727096699106685078573279839390298173709578624268600451946293387224363115670728098191131009772027543274109023367955314354736027939878547061225671274884832562367167702504120948949596, 33613816369065463469083237207724332433308634235300724690333242806098778374083852913453868425202855789825696265532575485120427816555368438518467128751373555434280565799981869998919509216604243882779260907751190222667239235345206726428293266825711227621257335585339059568863164447742085038678497850969525575174994652402595097801148321863588138581797997309939722523481755753013447489398234382743779547159433437068254459546074461205768548599124466701509871978657025810], 'aut_phi_ratio': 105.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 105, 2, 1], [3, 2, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [15, 2, 4, 1], [19, 1, 18, 1], [21, 2, 6, 1], [22, 1, 10, 1], [22, 105, 20, 1], [30, 2, 4, 1], [33, 2, 10, 1], [35, 2, 12, 1], [38, 1, 18, 1], [38, 105, 36, 1], [42, 2, 6, 1], [55, 2, 20, 1], [57, 2, 18, 1], [66, 2, 10, 1], [70, 2, 12, 1], [77, 2, 30, 1], [95, 2, 36, 1], [105, 2, 24, 1], [110, 2, 20, 1], [114, 2, 18, 1], [133, 2, 54, 1], [154, 2, 30, 1], [165, 2, 40, 1], [190, 2, 36, 1], [209, 1, 180, 1], [210, 2, 24, 1], [231, 2, 60, 1], [266, 2, 54, 1], [285, 2, 72, 1], [330, 2, 40, 1], [385, 2, 120, 1], [399, 2, 108, 1], [418, 1, 180, 1], [418, 105, 360, 1], [462, 2, 60, 1], [570, 2, 72, 1], [627, 2, 180, 1], [665, 2, 216, 1], [770, 2, 120, 1], [798, 2, 108, 1], [1045, 2, 360, 1], [1155, 2, 240, 1], [1254, 2, 180, 1], [1330, 2, 216, 1], [1463, 2, 540, 1], [1995, 2, 432, 1], [2090, 2, 360, 1], [2310, 2, 240, 1], [2926, 2, 540, 1], [3135, 2, 720, 1], [3990, 2, 432, 1], [4389, 2, 1080, 1], [6270, 2, 720, 1], [7315, 2, 2160, 1], [8778, 2, 1080, 1], [14630, 2, 2160, 1], [21945, 2, 4320, 1], [43890, 2, 4320, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\times C_{90}\\times F_5\\times S_3\\times F_7', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 90, 'autcent_group': '360.50', 'autcent_hash': 50, 'autcent_nilpotent': True, 'autcent_order': 360, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times C_{90}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 420, 'autcentquo_group': '5040.bh', 'autcentquo_hash': 3346192685167362256, 'autcentquo_nilpotent': False, 'autcentquo_order': 5040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 105, 2], [3, 2, 1], [5, 2, 2], [6, 2, 1], [7, 2, 3], [10, 2, 2], [11, 1, 10], [14, 2, 3], [15, 2, 4], [19, 1, 18], [21, 2, 6], [22, 1, 10], [22, 105, 20], [30, 2, 4], [33, 2, 10], [35, 2, 12], [38, 1, 18], [38, 105, 36], [42, 2, 6], [55, 2, 20], [57, 2, 18], [66, 2, 10], [70, 2, 12], [77, 2, 30], [95, 2, 36], [105, 2, 24], [110, 2, 20], [114, 2, 18], [133, 2, 54], [154, 2, 30], [165, 2, 40], [190, 2, 36], [209, 1, 180], [210, 2, 24], [231, 2, 60], [266, 2, 54], [285, 2, 72], [330, 2, 40], [385, 2, 120], [399, 2, 108], [418, 1, 180], [418, 105, 360], [462, 2, 60], [570, 2, 72], [627, 2, 180], [665, 2, 216], [770, 2, 120], [798, 2, 108], [1045, 2, 360], [1155, 2, 240], [1254, 2, 180], [1330, 2, 216], [1463, 2, 540], [1995, 2, 432], [2090, 2, 360], [2310, 2, 240], [2926, 2, 540], [3135, 2, 720], [3990, 2, 432], [4389, 2, 1080], [6270, 2, 720], [7315, 2, 2160], [8778, 2, 1080], [14630, 2, 2160], [21945, 2, 4320], [43890, 2, 4320]], 'center_label': '418.4', 'center_order': 418, 'central_product': True, 'central_quotient': '210.11', 'commutator_count': None, 'commutator_label': '105.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '5.1', '7.1', '11.1', '19.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['19.1', 1], ['2.1', 1], ['210.11', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 105, 1, 2], [3, 2, 1, 1], [5, 2, 2, 1], [6, 2, 1, 1], [7, 2, 3, 1], [10, 2, 2, 1], [11, 1, 10, 1], [14, 2, 3, 1], [15, 2, 4, 1], [19, 1, 18, 1], [21, 2, 6, 1], [22, 1, 10, 1], [22, 105, 10, 2], [30, 2, 4, 1], [33, 2, 10, 1], [35, 2, 12, 1], [38, 1, 18, 1], [38, 105, 18, 2], [42, 2, 6, 1], [55, 2, 20, 1], [57, 2, 18, 1], [66, 2, 10, 1], [70, 2, 12, 1], [77, 2, 30, 1], [95, 2, 36, 1], [105, 2, 24, 1], [110, 2, 20, 1], [114, 2, 18, 1], [133, 2, 54, 1], [154, 2, 30, 1], [165, 2, 40, 1], [190, 2, 36, 1], [209, 1, 180, 1], [210, 2, 24, 1], [231, 2, 60, 1], [266, 2, 54, 1], [285, 2, 72, 1], [330, 2, 40, 1], [385, 2, 120, 1], [399, 2, 108, 1], [418, 1, 180, 1], [418, 105, 180, 2], [462, 2, 60, 1], [570, 2, 72, 1], [627, 2, 180, 1], [665, 2, 216, 1], [770, 2, 120, 1], [798, 2, 108, 1], [1045, 2, 360, 1], [1155, 2, 240, 1], [1254, 2, 180, 1], [1330, 2, 216, 1], [1463, 2, 540, 1], [1995, 2, 432, 1], [2090, 2, 360, 1], [2310, 2, 240, 1], [2926, 2, 540, 1], [3135, 2, 720, 1], [3990, 2, 432, 1], [4389, 2, 1080, 1], [6270, 2, 720, 1], [7315, 2, 2160, 1], [8778, 2, 1080, 1], [14630, 2, 2160, 1], [21945, 2, 4320, 1], [43890, 2, 4320, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 720, 'exponent': 43890, 'exponents_of_order': [2, 1, 1, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7, 11, 19], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '87780.b', 'hash': 1882754446348593155, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 105], 'inner_gens': [[1, 838], [86945, 2]], 'inner_hash': 11, 'inner_nilpotent': False, 'inner_order': 210, 'inner_split': True, 'inner_tex': 'D_{105}', 'inner_used': [1, 2], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '87780.b', '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': True, 'monomial': True, 'name': 'C209*D210', '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, 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': 68, 'number_characteristic_subgroups': 68, 'number_conjugacy_classes': 22572, 'number_divisions': 72, 'number_normal_subgroups': 76, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 160, 'number_subgroups': 2368, 'old_label': None, 'order': 87780, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 211], [3, 2], [5, 4], [6, 2], [7, 6], [10, 4], [11, 10], [14, 6], [15, 8], [19, 18], [21, 12], [22, 2110], [30, 8], [33, 20], [35, 24], [38, 3798], [42, 12], [55, 40], [57, 36], [66, 20], [70, 24], [77, 60], [95, 72], [105, 48], [110, 40], [114, 36], [133, 108], [154, 60], [165, 80], [190, 72], [209, 180], [210, 48], [231, 120], [266, 108], [285, 144], [330, 80], [385, 240], [399, 216], [418, 37980], [462, 120], [570, 144], [627, 360], [665, 432], [770, 240], [798, 216], [1045, 720], [1155, 480], [1254, 360], [1330, 432], [1463, 1080], [1995, 864], [2090, 720], [2310, 480], [2926, 1080], [3135, 1440], [3990, 864], [4389, 2160], [6270, 1440], [7315, 4320], [8778, 2160], [14630, 4320], [21945, 8640], [43890, 8640]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 180, 'outer_gen_orders': [180, 90, 180, 60, 90, 180], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 73846], [43891, 202], [43891, 48614], [43891, 55274], [1, 64322], [1, 2894]], 'outer_group': None, 'outer_hash': 3183331083129895179, 'outer_nilpotent': True, 'outer_order': 8640, 'outer_permdeg': 29, 'outer_perms': [403911916827086772651739056, 305291636072840466184070477584, 305291636080139172208600397553, 304888965062676543257261817690, 620448401733286421837553, 621579701167061383807290], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_6\\times C_{180}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 47, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 11, 19], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '326170906360152851333218179981969164275240420482555559046255', 'gens': [1, 2], 'pres': [7, -2, -2, -3, -5, -7, -11, -19, 11733, 36, 35198, 79, 140787, 164, 879904, 277, 502]}, 'GLFp': {'d': 2, 'p': 419, 'gens': [16755464133, 30748104663]}, 'Perm': {'d': 47, 'gens': [5624964506810915667389970728440018332398525666304249927292, 20936201973436]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 418], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{209}\\times D_{210}', 'transitive_degree': 43890, 'wreath_data': None, 'wreath_product': False}
