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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '26244.fe', 'ambient_counter': 135, 'ambient_order': 26244, 'ambient_tex': 'C_3^6:(C_6\\times S_3)', 'central': False, 'central_factor': False, 'centralizer_order': 729, 'characteristic': False, 'core_order': 27, 'counter': 1168, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '26244.fe.972.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '972.c1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '972.445', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 445, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 972, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^3.S_3^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '27.5', 'subgroup_hash': 5, 'subgroup_order': 27, 'subgroup_tex': 'C_3^3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '26244.fe', 'aut_centralizer_order': None, 'aut_label': '972.C', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '36.A', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['324.A', '324.BW', '324.BZ', '324.CA', '324.CB', '324.CC', '324.CD', '324.CE', '486.S', '486.DC', '486.GD'], 'contains': ['2916.A', '2916.F', '2916.BU'], 'core': '972.C', 'coset_action_label': None, 'count': 2, 'diagramx': [1166, 4553, 5601, 4518], 'generators': [14076, 9828, 8748], 'label': '26244.fe.972.C', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '972.C', 'normal_contained_in': ['324.A'], 'normal_contains': ['2916.A'], 'normalizer': '1.a1', 'old_label': '972.c1', 'projective_image': '26244.fe', 'quotient_action_image': '36.12', 'quotient_action_kernel': '27.5', 'quotient_action_kernel_order': 27, 'quotient_fusion': None, 'short_label': '972.C', 'subgroup_fusion': None, 'weyl_group': '36.12'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '27.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 312, 'aut_gen_orders': [2, 13], 'aut_gens': [[1, 3, 9], [6, 2, 9], [5, 17, 11]], 'aut_group': '11232.a', 'aut_hash': 778507202365856770, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11232, 'aut_permdeg': 15, 'aut_perms': [6452863345, 297839648544], 'aut_phi_ratio': 624.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [3, 1, 26, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(3,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 312, 'autcent_group': '11232.a', 'autcent_hash': 778507202365856770, 'autcent_nilpotent': False, 'autcent_order': 11232, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(3,3)', '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], [3, 1, 26]], 'center_label': '27.5', 'center_order': 27, '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': ['3.1', '3.1', '3.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 13]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [3], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '27.5', 'hash': 5, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 3, 9], [1, 3, 9], [1, 3, 9]], '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, 27]], 'label': '27.5', 'linC_count': 1872, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 234, 'linQ_dim': 6, 'linQ_dim_count': 234, 'linR_count': 234, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^3', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 27, 'number_divisions': 14, 'number_normal_subgroups': 28, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 28, 'number_subgroups': 28, 'old_label': None, 'order': 27, 'order_factorization_type': 3, 'order_stats': [[1, 1], [3, 26]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 312, 'outer_gen_orders': [2, 13], 'outer_gen_pows': [0, 0], 'outer_gens': [[6, 2, 9], [5, 17, 11]], 'outer_group': '11232.a', 'outer_hash': 778507202365856770, 'outer_nilpotent': False, 'outer_order': 11232, 'outer_permdeg': 15, 'outer_perms': [6452863345, 297839648544], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(3,3)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 9, 'pgroup': 3, 'primary_abelian_invariants': [3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 13]], 'representations': {'PC': {'code': 0, 'gens': [1, 2, 3], 'pres': [3, -3, 3, 3]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [41624334336939899, 125101725607167719, 125101750005091125]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [10475581, 9534373, 23068812]}, 'Perm': {'d': 9, 'gens': [80640, 240, 4]}}, 'schur_multiplier': [3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3', 'transitive_degree': 27, '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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [6, 6, 6, 18], 'aut_gens': [[1, 6, 36, 108, 324, 972, 2916], [4853, 438, 11628, 108, 20304, 18468, 23760], [8317, 24162, 9792, 1188, 11556, 9720, 13464], [13265, 20478, 11628, 8964, 19980, 1944, 14220], [21833, 5730, 18396, 1188, 19764, 9720, 24120]], 'aut_group': '2304.fi', 'aut_hash': 5619012159166860013, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 472392, 'aut_permdeg': 324, 'aut_perms': [208279388942653345229744279750569979289322946613737375088907269712368142178259971884804215215148752251647976638721555850665379797829200741419135336979705559044307168193778260794963474702987112917954690219167428586859724353101762764654622084327187069643851893941339079666018249479327709436415755299459831614225702105482146727559260893106492849122272498642741019714710721081684497118677644743644955683764940750735937263778856821503605717392284087534511410168407211982530123993685348733025563227738578753687113949760104260641452966801962558414503903740862182701754891629270263329613018276949101278942291610847560588877833127358181252503237248352030146455811127145077889151619274, 88381683251365137520700582607203968790567031146307224322642452918502130721354963970182489187931595905336569971700253914456218471408400892807030502864272916973501550099817103500669290451215742166389146505758099081626291734321058461039023535870799655645595680865904339490108184132650561090006820594563699517782091124506278702606262237790292751810247296220738235796015989063915819827251481650529279801959297313219396365174892162487620429555965468013658788571078540838276950010878038388896618239207932169369159969251433357447739806040722850381354560234406925245174048888872752407218077348337069720365772564589950146582199314401099718158126074777661110344662137380632942337064828, 91184526486048505771752739158530735087146667190279253313115550412180479615390447776034106368173141066971132972175769242428343669905520132486642998617279267487623600036622196210361513936239722118663110015729352090231811386722508637914445675432413825541400565527949981052889537758824462608176694699088593839603912228571476071435202442155863756608149724270536634025987993088130596884032776875774447367090400809309325934296997052507842638337702889594165658881214437376162040419136014740315088545166438148347822288960429224275247462407112245094276905975294789367390810709803836215406092394576959898291169926688253658204869334813606844828541897833352257006363852635824853390004639, 134862440599069250304534964000696288071689989661436627455065808014575637193476983064667399640502079052963536048055007317855632907306367936813862857818914432445421833134110016902968473905051734907978099843257218465584710296031414400019663186012635525257482026957661085783717560947823987012088951539022302904564029336118949283542831289528282886696447432512329602187022167211046409697206044212565107044682795116272107495327629476711863589252866038285507559206457587444420089373300739883668587093980123774561668317113237535489887724858172647988965021382718341214654101003363666382545305128148084465308091819180778012396156764027688664898843783787614982284873839795934022232554675], 'aut_phi_ratio': 54.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 243, 1, 1], [2, 729, 1, 1], [3, 2, 1, 1], [3, 6, 1, 2], [3, 6, 3, 1], [3, 12, 1, 1], [3, 18, 1, 1], [3, 18, 2, 1], [3, 18, 9, 1], [3, 27, 2, 1], [3, 36, 1, 1], [3, 36, 3, 1], [3, 36, 9, 1], [3, 54, 2, 1], [3, 162, 1, 1], [3, 162, 2, 2], [3, 162, 6, 1], [6, 54, 1, 1], [6, 54, 3, 1], [6, 162, 1, 1], [6, 162, 2, 1], [6, 162, 9, 1], [6, 243, 2, 1], [6, 486, 1, 1], [6, 486, 2, 1], [6, 486, 6, 1], [6, 729, 2, 2], [6, 1458, 1, 2], [6, 1458, 2, 2], [9, 324, 1, 1], [9, 324, 2, 1], [9, 972, 1, 1], [9, 972, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6.S_3^2', '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': 18, 'autcentquo_group': None, 'autcentquo_hash': 5619012159166860013, 'autcentquo_nilpotent': False, 'autcentquo_order': 472392, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^5.C_3^5.C_2^3', 'cc_stats': [[1, 1, 1], [2, 27, 1], [2, 243, 1], [2, 729, 1], [3, 2, 1], [3, 6, 5], [3, 12, 1], [3, 18, 12], [3, 27, 2], [3, 36, 13], [3, 54, 2], [3, 162, 11], [6, 54, 4], [6, 162, 12], [6, 243, 2], [6, 486, 9], [6, 729, 4], [6, 1458, 6], [9, 324, 3], [9, 972, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '26244.fe', 'commutator_count': 1, 'commutator_label': '2187.2052', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 135, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 27, 1, 1], [2, 243, 1, 1], [2, 729, 1, 1], [3, 2, 1, 1], [3, 6, 1, 5], [3, 12, 1, 1], [3, 18, 1, 12], [3, 27, 2, 1], [3, 36, 1, 13], [3, 54, 2, 1], [3, 162, 1, 1], [3, 162, 2, 5], [6, 54, 1, 4], [6, 162, 1, 12], [6, 243, 2, 1], [6, 486, 1, 1], [6, 486, 2, 4], [6, 729, 2, 2], [6, 1458, 1, 2], [6, 1458, 2, 2], [9, 324, 1, 1], [9, 324, 2, 1], [9, 972, 1, 1], [9, 972, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 216, 'exponent': 18, 'exponents_of_order': [8, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 18], [36, 1, 9]], 'familial': False, 'frattini_label': '243.67', 'frattini_quotient': '108.38', 'hash': 759850994578172314, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [6, 6, 3, 3, 3, 3, 9], 'inner_gens': [[1, 24906, 9252, 2052, 19008, 10692, 6804], [12829, 6, 2556, 9936, 18144, 972, 21888], [20377, 18330, 36, 17604, 11016, 972, 11880], [973, 19662, 8784, 108, 324, 972, 20412], [10801, 9402, 18504, 108, 324, 972, 13608], [19441, 6, 36, 108, 324, 972, 2916], [25273, 11382, 144, 8856, 18792, 972, 2916]], 'inner_hash': 759850994578172314, 'inner_nilpotent': False, 'inner_order': 26244, 'inner_split': True, 'inner_tex': 'C_3^6:(C_6\\times S_3)', 'inner_used': [1, 2], 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 12], [2, 12], [4, 3], [6, 26], [12, 4], [18, 24], [36, 13]], 'label': '26244.fe', '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': True, 'name': 'C3^6:(C6*S3)', 'ngens': 10, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 40, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 94, 'number_divisions': 76, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 1798, 'number_subgroup_classes': 9686, 'number_subgroups': 2381393, 'old_label': None, 'order': 26244, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 999], [3, 2672], [6, 18684], [9, 3888]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [6, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[14981, 7422, 252, 1188, 2484, 972, 15048], [1, 8754, 36, 108, 324, 972, 2916]], 'outer_group': '18.3', 'outer_hash': 3, 'outer_nilpotent': False, 'outer_order': 18, 'outer_permdeg': 6, 'outer_perms': [690, 148], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3\\times S_3', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 5], [6, 10], [8, 1], [12, 10], [18, 24], [24, 1], [36, 13]], 'representations': {'PC': {'code': '1894592811385592501384948439613432022215722655288182165700539282028050669747742508269335277996423586859864324188313476897116805896921598148220287', 'gens': [1, 3, 5, 6, 7, 8, 9], 'pres': [10, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 20, 747182, 219882, 82, 888003, 415693, 462604, 30614, 21324, 75334, 123125, 528135, 99385, 29385, 1330566, 355336, 211706, 21466, 855367, 388817, 612368, 962298, 328348, 93188, 29748, 17068, 3848, 358, 1749609]}, 'Perm': {'d': 27, 'gens': [9615036051189125037688037065, 4581661241445977930397188975, 5839984708019093474217625675]}}, 'schur_multiplier': [3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^6:(C_6\\times S_3)', 'transitive_degree': 27, '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': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 18, 'aut_gen_orders': [2, 3, 3, 3, 3, 3, 2], 'aut_gens': [[16278328, 24577758, 1305911, 2939606, 36731395, 2794152, 29360962], [16278328, 7138662, 4514243, 2939606, 36731395, 11391087, 29360962], [33540394, 24577758, 1305911, 2939606, 36731395, 42750594, 22071741], [17852974, 24577758, 1305911, 2939606, 11537230, 11172560, 17852999], [16278328, 24577758, 1305911, 2939606, 36731395, 20646627, 16278362], [16278328, 24577758, 41439590, 2939606, 36731395, 2794152, 29360962], [4314670, 32864349, 35469088, 43014227, 36731395, 2794152, 4750707], [16278328, 20201582, 29656017, 32864349, 36731395, 14853248, 29360962]], 'aut_group': '972.445', 'aut_hash': 445, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 972, 'aut_permdeg': 36, 'aut_perms': [331093143824985607273236522129984378314067, 13633213040008548063764286135025081711792, 225232583683157182508650447566751140637897, 53969143714621496993854795574035405836775, 153784469452389964328765297048291929440, 262107881910387795571638951518569941715677, 335860263482059789150588035461216128168276], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 27, 1, 2], [3, 2, 1, 1], [3, 3, 1, 2], [3, 6, 1, 3], [3, 18, 1, 6], [6, 18, 1, 1], [6, 27, 1, 6], [6, 54, 1, 9], [9, 36, 1, 3]], 'aut_supersolvable': True, 'aut_tex': 'C_3^3.S_3^2', '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': 18, 'autcentquo_group': '972.445', 'autcentquo_hash': 445, 'autcentquo_nilpotent': False, 'autcentquo_order': 972, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_3^3.S_3^2', 'cc_stats': [[1, 1, 1], [2, 9, 1], [2, 27, 2], [3, 2, 1], [3, 3, 2], [3, 6, 3], [3, 18, 6], [6, 18, 1], [6, 27, 6], [6, 54, 9], [9, 36, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '972.445', 'commutator_count': 1, 'commutator_label': '81.7', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 445, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 1], [2, 27, 1, 2], [3, 2, 1, 1], [3, 3, 2, 1], [3, 6, 1, 1], [3, 6, 2, 1], [3, 18, 1, 2], [3, 18, 2, 2], [6, 18, 1, 1], [6, 27, 2, 3], [6, 54, 1, 3], [6, 54, 2, 3], [9, 36, 1, 1], [9, 36, 2, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 144, 'exponent': 18, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 2]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '108.38', 'hash': 445, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 18, 'inner_gen_orders': [2, 3, 3, 3, 3, 3, 2], 'inner_gens': [[16278328, 7138662, 4514243, 2939606, 36731395, 11391087, 29360962], [33540394, 24577758, 1305911, 2939606, 36731395, 20646627, 33540338], [17852974, 24577758, 1305911, 2939606, 11537230, 14853248, 1542375], [16278328, 24577758, 1305911, 2939606, 36731395, 42750594, 4750707], [16278328, 24577758, 41439590, 2939606, 36731395, 2794152, 29360962], [26377288, 7138662, 31289712, 20201582, 36731395, 2794152, 16278362], [16278328, 20201582, 29656017, 32864349, 36731395, 14853248, 29360962]], 'inner_hash': 445, 'inner_nilpotent': False, 'inner_order': 972, 'inner_split': True, 'inner_tex': 'C_3^3.S_3^2', 'inner_used': [1, 2, 3, 5, 6, 7], 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 12], [2, 12], [4, 3], [6, 6], [18, 2]], 'label': '972.445', 'linC_count': 2, 'linC_degree': 18, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 18, 'linQ_degree_count': 2, 'linQ_dim': 18, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 18, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^3.S3^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 35, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 35, 'number_divisions': 24, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 153, 'number_subgroup_classes': 153, 'number_subgroups': 1840, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 63], [3, 134], [6, 666], [9, 108]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 5], [6, 2], [8, 1], [12, 2], [18, 2]], 'representations': {'PC': {'code': 37775847321378497257394809683840891619295919, 'gens': [1, 3, 5, 6, 7], 'pres': [7, -2, -3, -2, -3, -3, -3, 3, 14, 5168, 2340, 58, 3699, 1690, 5478, 2335, 9077, 31758, 5312, 622]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [16278328, 24577758, 1305911, 2939606, 36731395, 2794152, 29360962]}, 'Perm': {'d': 27, 'gens': [81081325226784534221250, 15512334169126899406221385, 376703666922484, 7550102686338507196661760000, 2516538717432998141660098080, 418802676036117248219142964, 806634631153204606767248884]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^3.S_3^2', 'transitive_degree': 27, 'wreath_data': None, 'wreath_product': False}
