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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '3557376.a', 'ambient_counter': 1, 'ambient_order': 3557376, 'ambient_tex': 'C_{18528}.C_{192}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 111168, 'counter': 199, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '3557376.a.32._.BH', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '32.BH', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '32.16', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 32, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{16}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '111168.c', 'subgroup_hash': None, 'subgroup_order': 111168, 'subgroup_tex': 'C_{1158}:C_{96}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '3557376.a', 'aut_centralizer_order': None, 'aut_label': None, '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': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [18432, 1185792, 1778688, 4626, 64, 976992, 1225764, 147528, 921744], 'label': '3557376.a.32._.BH', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '32.BH', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '32._.BH', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '576.1364', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 37056, 'aut_gen_orders': [64, 64, 96, 24], 'aut_gens': [[1, 96], [93217, 98400], [7009, 6816], [87169, 76512], [13729, 57120]], 'aut_group': None, 'aut_hash': 5408501734751148099, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 444672, 'aut_permdeg': 965, 'aut_perms': 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'aut_phi_ratio': 12.0625, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 1, 2, 1], [3, 193, 3, 2], [4, 193, 1, 4], [6, 1, 2, 1], [6, 193, 2, 2], [6, 193, 3, 6], [8, 193, 1, 8], [12, 193, 2, 4], [12, 193, 3, 8], [16, 193, 1, 16], [24, 193, 2, 8], [24, 193, 3, 16], [32, 193, 2, 16], [48, 193, 2, 16], [48, 193, 3, 32], [96, 193, 4, 16], [96, 193, 6, 32], [193, 96, 2, 1], [386, 96, 2, 1], [579, 96, 4, 1], [1158, 96, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{579}.C_{96}.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '12.4', 'autcent_hash': 4, 'autcent_nilpotent': False, 'autcent_order': 12, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 37056, 'autcentquo_group': '37056.a', 'autcentquo_hash': 1432757702296672986, 'autcentquo_nilpotent': False, 'autcentquo_order': 37056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{193}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 193, 2], [3, 1, 2], [3, 193, 6], [4, 193, 4], [6, 1, 2], [6, 193, 22], [8, 193, 8], [12, 193, 32], [16, 193, 16], [24, 193, 64], [32, 193, 32], [48, 193, 128], [96, 193, 256], [193, 96, 2], [386, 96, 2], [579, 96, 4], [1158, 96, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '18528.c', 'commutator_count': 1, 'commutator_label': '193.1', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['18528.c', 1], ['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 1, 2, 1], [3, 193, 2, 3], [4, 193, 2, 2], [6, 1, 2, 1], [6, 193, 2, 11], [8, 193, 4, 2], [12, 193, 4, 8], [16, 193, 8, 2], [24, 193, 8, 8], [32, 193, 16, 2], [48, 193, 16, 8], [96, 193, 32, 8], [193, 96, 2, 1], [386, 96, 2, 1], [579, 96, 4, 1], [1158, 96, 4, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6144, 'exponent': 18528, 'exponents_of_order': [6, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': [[96, 0, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '111168.c', 'hash': 5741594154914542696, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18528, 'inner_gen_orders': [96, 193], 'inner_gens': [[1, 16800], [94465, 96]], 'inner_hash': 5691368528950376625, 'inner_nilpotent': False, 'inner_order': 18528, 'inner_split': False, 'inner_tex': 'C_{193}:C_{96}', 'inner_used': [1, 2], 'irrC_degree': 96, 'irrQ_degree': 384, 'irrQ_dim': 384, 'irrR_degree': None, 'irrep_stats': [[1, 576], [96, 12]], 'label': '111168.c', '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': 'C1158:C96', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 196, 'number_characteristic_subgroups': 49, 'number_conjugacy_classes': 588, 'number_divisions': 64, 'number_normal_subgroups': 106, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 204, 'number_subgroups': 19020, 'old_label': None, 'order': 111168, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 387], [3, 1160], [4, 772], [6, 4248], [8, 1544], [12, 6176], [16, 3088], [24, 12352], [32, 6176], [48, 24704], [96, 49408], [193, 192], [386, 192], [579, 384], [1158, 384]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 75], 'outer_gens': [[55585, 36960], [74113, 111072], [74113, 12192]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [7, 120, 856], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 198, 'pgroup': 0, 'primary_abelian_invariants': [2, 32, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 18], [4, 10], [8, 10], [16, 10], [32, 8], [192, 2], [384, 2]], 'representations': {'PC': {'code': '8470973334695474248797610233160581190528376460099202906569931456515871758068570160805163442882713084197849198411092670883514320098582218256185017261989036415', 'gens': [1, 7], 'pres': [9, -2, -2, -2, -2, -2, -3, -2, -3, -193, 18, 46, 74, 102, 130, 1058406, 1563423, 1434912, 631293, 41244, 56940, 186, 2419207, 3573520, 1278745, 442402, 94219, 130084, 286, 8164808, 3055985, 2064554, 367451, 317888, 157517]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 1164627283, 783607298]}, 'Perm': {'d': 198, 'gens': [101094670908187785394279178056400703055889861415861904023442093415716138113688448493959179476063732730238025472440789831819918066491607924436058150015716801676832301651665420700619108216469388440446771485335959808182459626747141245041157588709459355285979540088004466191962691147678685264316560016931124094024379270825211416064176698851077303784345956390947885876412160, 1550209885149356170855342979531720019629263526157145049430781486599308546945950775874914232673081481701458819188662784332576230398932364604294107603488070602426942547616092097362417484288398289051727405425109452885230066034303600877125670666789599987117836007886329167548474411055126081341023640629569032699145482038494188498398020265019443856170385796419262188019791, 2060826462767096546544079795749596996143301944853286064465219999285593862557871695738394162981539201095610810306457064122370449596700976786449204798811583094111842224919484222332685742449579146922112497711821446951935850122918007574144701264394981639685114545506357799668405171318316362372334252828564377302902869148512376246296320328901923527766808448739964030865249]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6, 96], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{1158}:C_{96}', 'transitive_degree': 1158, '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': '18432.b', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 192], [876481, 1429440], [3069121, 3456960], [57985, 2080704], [2142913, 1063488], [888385, 1160256], [393793, 1965120]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 113836032, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 96.5, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 193, 2], [3, 1, 2], [3, 193, 6], [4, 1, 2], [4, 193, 10], [6, 1, 2], [6, 193, 22], [8, 1, 4], [8, 193, 44], [12, 1, 4], [12, 193, 92], [16, 1, 8], [16, 193, 184], [24, 1, 8], [24, 193, 376], [32, 1, 16], [32, 193, 752], [48, 1, 16], [48, 193, 1520], [64, 193, 1024], [96, 1, 32], [96, 193, 6112], [192, 193, 8192], [193, 192, 1], [386, 192, 1], [579, 192, 2], [772, 192, 2], [1158, 192, 2], [1544, 192, 4], [2316, 192, 4], [3088, 192, 8], [4632, 192, 8], [6176, 192, 16], [9264, 192, 16], [18528, 192, 32]], 'center_label': '96.2', 'center_order': 96, 'central_product': None, 'central_quotient': '37056.a', 'commutator_count': None, 'commutator_label': '193.1', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '193.1'], 'composition_length': 14, 'conjugacy_classes_known': False, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 193, 1, 2], [3, 1, 2, 1], [3, 193, 2, 3], [4, 1, 2, 1], [4, 193, 2, 5], [6, 1, 2, 1], [6, 193, 2, 11], [8, 1, 4, 1], [8, 193, 4, 11], [12, 1, 4, 1], [12, 193, 4, 23], [16, 1, 8, 1], [16, 193, 8, 23], [24, 1, 8, 1], [24, 193, 8, 47], [32, 1, 16, 1], [32, 193, 16, 47], [48, 1, 16, 1], [48, 193, 16, 95], [64, 193, 32, 32], [96, 1, 32, 1], [96, 193, 32, 191], [192, 193, 64, 128], [193, 192, 1, 1], [386, 192, 1, 1], [579, 192, 2, 1], [772, 192, 2, 1], [1158, 192, 2, 1], [1544, 192, 4, 1], [2316, 192, 4, 1], [3088, 192, 8, 1], [4632, 192, 8, 1], [6176, 192, 16, 1], [9264, 192, 16, 1], [18528, 192, 32, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': None, 'exponent': 37056, 'exponents_of_order': [11, 2, 1], 'factors_of_aut_order': [2, 3, 193], 'factors_of_order': [2, 3, 193], 'faithful_reps': None, 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '222336.a', 'hash': 4558118773988019320, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [192, 193], 'inner_gens': [[1, 995520], [2562049, 192]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 37056, 'inner_split': None, 'inner_tex': 'F_{193}', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '3557376.a', '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': 'C18528.C192', 'ngens': 14, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 4, 0, 7, 0, 0, 12, 0, 15, 1, 0, 0, 28, 0, 31, 3, 0, 60, 0, 63, 7, 0, 124, 63, 15, 0, 252, 31, 31, 252, 15, 63, 124, 7, 63, 60, 3, 31, 28, 1, 15, 12, 7, 4, 3, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 138, 'number_conjugacy_classes': 18528, 'number_divisions': 642, 'number_normal_subgroups': 1452, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 3557376, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 387], [3, 1160], [4, 1932], [6, 4248], [8, 8496], [12, 17760], [16, 35520], [24, 72576], [32, 145152], [48, 293376], [64, 197632], [96, 1179648], [192, 1581056], [193, 192], [386, 192], [579, 384], [772, 384], [1158, 384], [1544, 768], [2316, 768], [3088, 1536], [4632, 1536], [6176, 3072], [9264, 3072], [18528, 6144]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 3072, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [32, 64, 3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '182054418431007814350628784113035127425923799998549626324737447559099474473500212095784854959685208198956508708925754548976768011429404512891574259881681671221516751393913168065686356563808892270973000037766487093761654031433869714286538508197012735365514548618076002727100258032622909305370828966937134972730735153736039736031801992112423270146020575514718706769132929262778706691501037447094141129207654048030198545299388335059695198597258946583347266060671', 'gens': [1, 8], 'pres': [14, -2, -2, -2, -2, -2, -2, -3, -2, -2, -2, -2, -2, -3, -193, 28, 71, 114, 157, 200, 243, 111498247, 1042965, 50582819, 6711985, 12903807, 1613549, 871339, 329, 250871048, 2346646, 1753956, 15101906, 1019152, 3630390, 1960400, 372, 59458569, 5214743, 3897637, 33559731, 2264705, 8067439, 4356333, 415, 130808842, 11472408, 8574758, 5351860, 4982274, 628400, 1023886, 458, 285401099, 25030681, 18708519, 11676725, 10870339, 1370961, 2233823, 501, 618369036, 54233114, 40535080, 25299510, 23552324, 2970322, 4839840, 726, 603316237, 175214619, 130959401, 81736759, 32514117, 9596243, 4741729]}, 'GLFp': {'d': 2, 'p': 193, 'gens': [7189251, 35945286, 999278948]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [96, 192], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 256, 'supersolvable': True, 'sylow_subgroups_known': False, 'tex_name': 'C_{18528}.C_{192}', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '32.16', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [4, 2, 2, 4, 2], 'aut_gens': [[1, 2], [17, 15], [1, 3], [1, 30], [1, 10], [1, 14]], 'aut_group': '32.48', 'aut_hash': 48, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 32, 'aut_permdeg': 10, 'aut_perms': [455286, 374406, 1270441, 859248, 1], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [4, 1, 2, 2], [8, 1, 4, 2], [16, 1, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4:C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.48', 'autcent_hash': 48, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'D_4:C_2^2', '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, 3], [4, 1, 4], [8, 1, 8], [16, 1, 16]], 'center_label': '32.16', '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': 16, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 1, 2, 2], [8, 1, 4, 2], [16, 1, 8, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 12, 'exponent': 16, 'exponents_of_order': [5], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '4.2', 'hash': 16, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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': '32.16', 'linC_count': 192, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 9, 'linQ_degree_count': 4, 'linQ_dim': 9, 'linQ_dim_count': 4, 'linR_count': 16, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C16', 'ngens': 2, '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': 8, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 32, 'number_divisions': 10, 'number_normal_subgroups': 14, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 14, 'number_subgroups': 14, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 4], [8, 8], [16, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 2, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[17, 15], [1, 3], [1, 30], [1, 10], [1, 14]], 'outer_group': '32.48', 'outer_hash': 48, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [455286, 374406, 1270441, 859248, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 16], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 2], [8, 2]], 'representations': {'PC': {'code': 17891342, 'gens': [1, 2], 'pres': [5, -2, 2, -2, -2, -2, 26, 42, 58]}, 'GLFp': {'d': 2, 'p': 17, 'gens': [19665, 14742]}, 'Perm': {'d': 18, 'gens': [20916435456000, 355687428096000, 9703614452976, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 16], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{16}', 'transitive_degree': 32, 'wreath_data': None, 'wreath_product': False}
