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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '324000.v', 'ambient_counter': 22, 'ambient_order': 324000, 'ambient_tex': 'D_{15}\\wr S_3:C_2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1, 'counter': 604, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '324000.v.120.cl1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '120.cl1', 'outer_equivalence': True, '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': 120, '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': '2700.q', 'subgroup_hash': 8099013394032210383, 'subgroup_order': 2700, 'subgroup_tex': 'C_{15}^2:D_6', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '324000.v', 'aut_centralizer_order': None, 'aut_label': '120.cl1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['24.u1', '40.d1', '60.a1'], 'contains': [], 'core': '324000.a1', 'coset_action_label': None, 'count': 20, 'diagramx': None, 'generators': [28849, 211824, 96484, 480, 122646, 133920, 223680], 'label': '324000.v.120.cl1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.f1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '20.a1', 'old_label': '120.cl1', 'projective_image': '324000.v', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '120.cl1', 'subgroup_fusion': None, 'weyl_group': '5400.q'}
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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': 3, 'aut_exponent': 120, 'aut_gen_orders': [30, 8, 24, 24], 'aut_gens': [[1, 2, 12, 180], [2261, 1402, 168, 264], [431, 694, 2244, 1608], [2431, 302, 2244, 2484], [2119, 1510, 1644, 2364]], 'aut_group': None, 'aut_hash': 7509908978670635385, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21600, 'aut_permdeg': 90, 'aut_perms': [1223718560084616643378011208422965467506668793203639699838220593818746746451832335686901635315283618356704229363990232635125174632593337037, 1181674562415681112563614535571498175673032522628224692185802545653006757524643646115437306083046741477899046391560581345618446675707747838, 365485412783665425823287248426271448329414864055784104381614255917074554446401272649710462951220353102249428940907350473684225225077400145, 427414949721339587139027811969459071248455897039281133220302817737683668206477290996457252490043882635733454882249136064436272803425588382], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [2, 45, 2, 1], [3, 1, 2, 1], [3, 6, 1, 1], [3, 150, 3, 1], [5, 6, 4, 1], [6, 25, 2, 1], [6, 45, 4, 1], [6, 150, 1, 1], [6, 150, 3, 1], [10, 90, 4, 1], [15, 6, 8, 1], [15, 12, 4, 1], [15, 12, 8, 1], [30, 90, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{15}^2.C_{12}.C_2^3', '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': 120, 'autcentquo_group': None, 'autcentquo_hash': 7509908978670635385, 'autcentquo_nilpotent': False, 'autcentquo_order': 21600, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{15}^2.C_{12}.C_2^3', 'cc_stats': [[1, 1, 1], [2, 25, 1], [2, 45, 2], [3, 1, 2], [3, 6, 1], [3, 150, 3], [5, 6, 4], [6, 25, 2], [6, 45, 4], [6, 150, 4], [10, 90, 4], [15, 6, 8], [15, 12, 12], [30, 90, 8]], 'center_label': '3.1', 'center_order': 3, 'central_product': False, 'central_quotient': '900.96', 'commutator_count': 1, 'commutator_label': '675.12', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '5.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [2, 45, 1, 2], [3, 1, 2, 1], [3, 6, 1, 1], [3, 150, 1, 3], [5, 6, 2, 2], [6, 25, 2, 1], [6, 45, 2, 2], [6, 150, 1, 4], [10, 90, 2, 2], [15, 6, 4, 2], [15, 12, 2, 2], [15, 12, 4, 2], [30, 90, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 353808, 'exponent': 30, 'exponents_of_order': [3, 2, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[6, 0, 16], [12, 0, 8]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '900.96', 'hash': 8099013394032210383, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [10, 6, 5, 15], 'inner_gens': [[1, 2290, 552, 2640], [137, 2, 2280, 204], [2161, 614, 12, 180], [421, 158, 12, 180]], 'inner_hash': 96, 'inner_nilpotent': False, 'inner_order': 900, 'inner_split': False, 'inner_tex': '(C_5\\times C_{15}):D_6', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 8], [3, 8], [6, 24], [12, 12]], 'label': '2700.q', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 16, 'linQ_dim': 18, 'linQ_dim_count': 16, 'linR_count': 40, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C15^2:D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 56, 'number_divisions': 28, 'number_normal_subgroups': 20, 'number_subgroup_autclasses': 78, 'number_subgroup_classes': 154, 'number_subgroups': 3982, 'old_label': None, 'order': 2700, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 115], [3, 458], [5, 24], [6, 830], [10, 360], [15, 192], [30, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 2274], 'outer_gens': [[1, 1234, 672, 780], [547, 2686, 588, 2028]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [120, 1457], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', '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, 4], [24, 6], [48, 2]], 'representations': {'PC': {'code': '1612142572079446564926954310253041976083279094358905608142674983885914487', 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 3, 3, 5, 3, 5, 4788, 32061, 36, 48302, 15459, 31930, 15473, 108, 57964, 18911, 10728, 110885, 4296, 19801, 166, 105846, 15007, 902]}, 'Perm': {'d': 24, 'gens': [28304768306459701734966, 4817187026792126393844, 55346845900579008695499]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{15}^2:D_6', 'transitive_degree': 45, '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': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 180, 'aut_gen_orders': [30, 12, 2, 30, 30, 15], 'aut_gens': [[1, 2, 12, 24, 720, 21600], [207793, 323002, 201384, 13656, 59748, 21696], [184565, 163622, 86328, 48912, 263556, 43392], [238129, 267770, 173148, 696, 720, 302400], [131329, 30170, 282780, 10104, 301680, 21600], [2725, 26726, 260652, 174264, 22320, 302400], [130129, 130130, 12, 24, 22320, 21600]], 'aut_group': '648000.v', 'aut_hash': 2811864275658790406, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 648000, 'aut_permdeg': 162, 'aut_perms': [4685510030374816950452778367108544809733980531595782858991872468654765052097008420103953855763976668232949508555035640474131150896964054463732183691249885335817074879195652953252949109490859904709094199258513422299083637331151088744299648469684985213049369085948376131311563334569512290463, 118810961353249954383259206324367203968736140373148055655275555774564259288656473735598876623747602329767652150153626504462567120206366963164744669741691257827457562435823539599889744462070652516244607956383997022627322988087200665923879957269978172940074719799530282584336410595484154612, 10475822386573938297452435805130966850773651702627564794046372048909068190754205633475427265406838461543658921558258299478822760510232579482097424184977666094656211303056837214559059580071614083789549146686413917572303671743263974053349418142035511794837379802494040697450995281403307619044, 10816314374897602576841246776871760873447680283460445432668110116154399765340789417297807526802655468241374105861178296371085439913984688535906968244972679752234400352198149209252083553758869709742925833504424320186079410591884635480038005578176128531688767882091323258415214439039947939691, 7077997557867542314304080792325451851049896144088706538222080028534582227413946564398330019225555761276699448496660647142346528606760862876999450607274683889129172108082749073333872207121459207040609751116516672601325843609242274882414572238351547973160995494168626106126443656437786952, 429975614670325991058705159366897708283358377317677080107920929042722773066373447441364459539277723764329056601292070607145303766112288543890492898594644369605681556494219527571401850809533847825905387332059744940466697303661552957066184233837058746871521292212100256304902280611782472], 'aut_phi_ratio': 7.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 225, 1, 1], [2, 270, 1, 1], [2, 450, 1, 1], [2, 675, 1, 1], [2, 1350, 1, 1], [2, 3375, 1, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 1350, 1, 1], [4, 4050, 1, 1], [4, 6750, 1, 1], [4, 20250, 1, 1], [5, 6, 2, 1], [5, 8, 2, 1], [5, 12, 2, 1], [5, 24, 1, 1], [5, 24, 2, 1], [6, 180, 1, 4], [6, 270, 1, 1], [6, 360, 1, 1], [6, 540, 1, 1], [6, 750, 1, 1], [6, 900, 1, 4], [6, 1000, 1, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 1800, 1, 1], [6, 2700, 1, 1], [6, 5400, 1, 1], [6, 9000, 1, 1], [6, 27000, 1, 1], [9, 3600, 1, 1], [10, 162, 2, 1], [10, 180, 2, 4], [10, 216, 2, 1], [10, 324, 2, 1], [10, 360, 1, 1], [10, 360, 2, 2], [10, 450, 2, 1], [10, 540, 2, 4], [10, 648, 1, 1], [10, 648, 2, 1], [10, 900, 2, 1], [10, 1080, 1, 1], [10, 1080, 2, 2], [10, 1350, 2, 1], [10, 2700, 2, 1], [12, 2700, 1, 1], [12, 13500, 1, 1], [15, 12, 2, 1], [15, 16, 2, 1], [15, 24, 2, 5], [15, 48, 1, 1], [15, 48, 2, 16], [15, 96, 2, 7], [15, 3600, 2, 1], [18, 18000, 1, 1], [20, 2700, 2, 1], [20, 8100, 2, 1], [30, 360, 2, 8], [30, 720, 2, 14], [30, 1080, 2, 4], [30, 1800, 2, 4], [30, 2160, 1, 1], [30, 2160, 2, 2], [30, 2700, 2, 1], [30, 3600, 2, 1], [30, 5400, 2, 1], [30, 10800, 2, 1], [45, 7200, 2, 1], [60, 5400, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'D_{15}\\wr S_3.C_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': 180, 'autcentquo_group': '648000.v', 'autcentquo_hash': 2811864275658790406, 'autcentquo_nilpotent': False, 'autcentquo_order': 648000, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'D_{15}\\wr S_3.C_4', 'cc_stats': [[1, 1, 1], [2, 27, 1], [2, 45, 1], [2, 90, 1], [2, 125, 1], [2, 135, 1], [2, 225, 1], [2, 270, 1], [2, 450, 1], [2, 675, 1], [2, 1350, 1], [2, 3375, 1], [3, 6, 1], [3, 8, 1], [3, 12, 1], [3, 1800, 1], [4, 1350, 1], [4, 4050, 1], [4, 6750, 1], [4, 20250, 1], [5, 6, 2], [5, 8, 2], [5, 12, 2], [5, 24, 3], [6, 180, 4], [6, 270, 1], [6, 360, 1], [6, 540, 1], [6, 750, 1], [6, 900, 4], [6, 1000, 1], [6, 1350, 1], [6, 1500, 1], [6, 1800, 1], [6, 2700, 1], [6, 5400, 1], [6, 9000, 1], [6, 27000, 1], [9, 3600, 1], [10, 162, 2], [10, 180, 8], [10, 216, 2], [10, 324, 2], [10, 360, 5], [10, 450, 2], [10, 540, 8], [10, 648, 3], [10, 900, 2], [10, 1080, 5], [10, 1350, 2], [10, 2700, 2], [12, 2700, 1], [12, 13500, 1], [15, 12, 2], [15, 16, 2], [15, 24, 10], [15, 48, 33], [15, 96, 14], [15, 3600, 2], [18, 18000, 1], [20, 2700, 2], [20, 8100, 2], [30, 360, 16], [30, 720, 28], [30, 1080, 8], [30, 1800, 8], [30, 2160, 5], [30, 2700, 2], [30, 3600, 2], [30, 5400, 2], [30, 10800, 2], [45, 7200, 2], [60, 5400, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '324000.v', 'commutator_count': 1, 'commutator_label': '40500.j', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '5.1', '5.1', '5.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 22, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 45, 1, 1], [2, 90, 1, 1], [2, 125, 1, 1], [2, 135, 1, 1], [2, 225, 1, 1], [2, 270, 1, 1], [2, 450, 1, 1], [2, 675, 1, 1], [2, 1350, 1, 1], [2, 3375, 1, 1], [3, 6, 1, 1], [3, 8, 1, 1], [3, 12, 1, 1], [3, 1800, 1, 1], [4, 1350, 1, 1], [4, 4050, 1, 1], [4, 6750, 1, 1], [4, 20250, 1, 1], [5, 6, 2, 1], [5, 8, 2, 1], [5, 12, 2, 1], [5, 24, 1, 1], [5, 24, 2, 1], [6, 180, 1, 4], [6, 270, 1, 1], [6, 360, 1, 1], [6, 540, 1, 1], [6, 750, 1, 1], [6, 900, 1, 4], [6, 1000, 1, 1], [6, 1350, 1, 1], [6, 1500, 1, 1], [6, 1800, 1, 1], [6, 2700, 1, 1], [6, 5400, 1, 1], [6, 9000, 1, 1], [6, 27000, 1, 1], [9, 3600, 1, 1], [10, 162, 2, 1], [10, 180, 2, 4], [10, 216, 2, 1], [10, 324, 2, 1], [10, 360, 1, 1], [10, 360, 2, 2], [10, 450, 2, 1], [10, 540, 2, 4], [10, 648, 1, 1], [10, 648, 2, 1], [10, 900, 2, 1], [10, 1080, 1, 1], [10, 1080, 2, 2], [10, 1350, 2, 1], [10, 2700, 2, 1], [12, 2700, 1, 1], [12, 13500, 1, 1], [15, 12, 2, 1], [15, 16, 2, 1], [15, 24, 2, 5], [15, 48, 1, 1], [15, 48, 2, 16], [15, 96, 2, 7], [15, 3600, 2, 1], [18, 18000, 1, 1], [20, 2700, 2, 1], [20, 8100, 2, 1], [30, 360, 2, 8], [30, 720, 2, 14], [30, 1080, 2, 4], [30, 1800, 2, 4], [30, 2160, 1, 1], [30, 2160, 2, 2], [30, 2700, 2, 1], [30, 3600, 2, 1], [30, 5400, 2, 1], [30, 10800, 2, 1], [45, 7200, 2, 1], [60, 5400, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 180, 'exponents_of_order': [5, 4, 3], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[12, 1, 8], [16, 1, 4], [24, 1, 42], [32, 1, 2], [48, 1, 66], [96, 1, 14]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '324000.v', 'hash': 8840609915906051830, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 180, 'inner_gen_orders': [6, 18, 10, 30, 30, 15], 'inner_gens': [[1, 213514, 87336, 16104, 137172, 86784], [43301, 2, 67176, 107904, 264132, 86784], [159349, 136310, 12, 160536, 85680, 21600], [6241, 215402, 185820, 24, 172080, 21600], [196933, 221654, 260652, 174264, 720, 302400], [259537, 259538, 12, 24, 43920, 21600]], 'inner_hash': 8840609915906051830, 'inner_nilpotent': False, 'inner_order': 324000, 'inner_split': False, 'inner_tex': 'D_{15}\\wr S_3:C_2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 12, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 4], [3, 8], [6, 24], [8, 12], [12, 38], [16, 10], [24, 54], [32, 2], [48, 66], [96, 14]], 'label': '324000.v', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'D15wrS3:C2', 'ngens': 12, '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, 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': 145, 'number_characteristic_subgroups': 31, 'number_conjugacy_classes': 240, 'number_divisions': 145, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 5684, 'number_subgroup_classes': 5684, 'number_subgroups': 3442352, 'old_label': None, 'order': 324000, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 6767], [3, 1826], [4, 32400], [5, 124], [6, 55990], [9, 3600], [10, 27108], [12, 16200], [15, 10424], [18, 18000], [20, 21600], [30, 104760], [45, 14400], [60, 10800]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [14406], 'outer_gens': [[4321, 223202, 47580, 168, 48240, 151200]], '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': 6, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [3, 8], [6, 8], [8, 4], [12, 18], [16, 6], [24, 18], [32, 4], [48, 27], [64, 1], [96, 32], [192, 7]], 'representations': {'PC': {'code': '7904243998201006819700278186742502956867267850921411190950211583056509783708101738338623454885725063291657712340478731105659115360674741429144862238404132271133550158517738149457918120251310384531600422127557464947267103218463649044676549897690995471900780088291169536499952934926706974803627123940471', 'gens': [1, 2, 4, 5, 8, 11], 'pres': [12, 2, 2, 3, 2, 2, 3, 5, 2, 3, 5, 3, 5, 2684160, 5124337, 61, 1451810, 1103786, 4192131, 1612239, 3867723, 259239, 966244, 3237136, 760888, 802720, 172, 38021, 10853585, 3214109, 1818473, 281, 8896626, 4445310, 1818474, 13168519, 12678355, 7402207, 685483, 688375, 606307, 173359, 283, 622088, 8164820, 7595888, 181484, 90776, 428, 2073609, 7776021, 5836353, 172845, 86457, 11455498, 5727766, 332674, 55534, 526, 37387019, 18693527, 311075, 51935]}, 'Perm': {'d': 24, 'gens': [51920595553715380090391, 81147167704888758168172, 26015509532645288463586]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 225, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_{15}\\wr S_3:C_2', 'transitive_degree': 45, 'wreath_data': None, 'wreath_product': False}
