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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '384.2088', 'ambient_counter': 2088, 'ambient_order': 384, 'ambient_tex': '(C_2^2\\times C_6).D_8', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': False, 'core_order': 24, 'counter': 61, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '384.2088.16.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '16.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '16.4', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 4, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 16, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4:C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '24.9', 'subgroup_hash': 9, 'subgroup_order': 24, 'subgroup_tex': 'C_2\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '384.2088', 'aut_centralizer_order': None, 'aut_label': '16.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '4.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['8.c1', '8.d1', '8.e1'], 'contains': ['32.a1', '32.m1', '48.e1'], 'core': '16.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [241, 192, 128, 32], 'label': '384.2088.16.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '16.e1', 'normal_contained_in': ['8.c1', '8.d1', '8.e1'], 'normal_contains': ['32.a1', '48.e1'], 'normalizer': '1.a1', 'old_label': '16.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '16.e1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2], 'aut_gens': [[1, 2], [13, 2], [1, 23], [1, 10], [1, 14]], 'aut_group': '16.11', 'aut_hash': 11, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 16, 'aut_permdeg': 6, 'aut_perms': [288, 6, 127, 126], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [12, 1, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '16.11', 'autcent_hash': 11, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times D_4', '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], [3, 1, 2], [4, 1, 4], [6, 1, 6], [12, 1, 8]], 'center_label': '24.9', 'center_order': 24, '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', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 9, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 2], [6, 1, 2, 3], [12, 1, 4, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 12, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '12.5', 'hash': 9, '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, 24]], 'label': '24.9', 'linC_count': 96, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 4, 'linQ_dim': 4, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C12', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 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': 8, 'number_conjugacy_classes': 24, 'number_divisions': 12, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 16, 'number_subgroups': 16, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [6, 6], [12, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[13, 2], [1, 23], [1, 10], [1, 14]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [288, 6, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 2]], 'representations': {'PC': {'code': 221281, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -3, 21, 34]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [35931072, 26129103]}, 'GLFp': {'d': 2, 'p': 13, 'gens': [10993, 4396]}, 'Perm': {'d': 9, 'gens': [2400, 40320, 4, 744]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], '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_{12}', 'transitive_degree': 24, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12, 4, 2, 6, 12, 12, 6, 6, 4], 'aut_gens': [[1, 2, 8, 64], [225, 226, 12, 64], [37, 215, 328, 64], [1, 199, 40, 320], [33, 54, 156, 320], [197, 214, 92, 64], [197, 211, 124, 64], [1, 18, 296, 64], [229, 34, 284, 64], [225, 55, 360, 64], [33, 247, 28, 64]], 'aut_group': None, 'aut_hash': 3386124555295775868, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 80, 'aut_perms': [203822524674470814250720874586669264048519357004329297435795799395555673815595311360616496886646574589083788399371093, 51483497994287835986721233923599058083776825841974548070722883543326597881516552922763661563294309723173127148497927409, 49675313759217988170764122962050339656046876854722516136703066517721837204030516992313888220599240941305626825874708870, 55810042337718404364985467485248283606935057494957831401755083410478767721519788057567408466686836035481643897170904639, 47462976219825574272840010497120284724432831879247510173559215905118710412974602019310707752306415338715100708383167762, 55049070941016669037999828223784028476854256450338824619184363440764126099253734789909236635922031413408348812070866851, 47615295735600564058351191491562343367660303271383998844749965337589171187290661089962798491703764774010664883146003766, 52052926622022639366067405829238767999623095548910212356749907158522043844647029247584972366234178533879202712986492542, 24498459644810803868295158469439630544667174474172588088245843819799976658364091001892350307491636639213236317968870953, 25035561541359491667653059837070988771496773356655158413274139028854146530371442052749630464710788612609364319588892416], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [2, 2, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 2, 4, 1], [4, 8, 4, 1], [4, 24, 4, 1], [6, 2, 1, 3], [6, 2, 2, 2], [6, 4, 4, 1], [8, 6, 8, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 4, 4, 1], [12, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^7.C_2^6)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '512.10494213', 'autcent_hash': 1718285292446712970, 'autcent_nilpotent': True, 'autcent_order': 512, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '48.51', 'autcentquo_hash': 51, 'autcentquo_nilpotent': False, 'autcentquo_order': 48, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [3, 2, 1], [4, 2, 8], [4, 8, 4], [4, 24, 4], [6, 2, 7], [6, 4, 4], [8, 6, 16], [12, 4, 8], [12, 8, 8]], 'center_label': '8.5', 'center_order': 8, 'central_product': False, 'central_quotient': '48.43', 'commutator_count': 1, 'commutator_label': '24.9', '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': 2088, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [3, 2, 1, 1], [4, 2, 1, 4], [4, 2, 2, 2], [4, 8, 2, 2], [4, 24, 2, 2], [6, 2, 1, 7], [6, 4, 1, 4], [8, 6, 2, 4], [8, 6, 4, 2], [12, 4, 1, 4], [12, 4, 2, 2], [12, 8, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '24.14', 'hash': 2088, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 4, 3], 'inner_gens': [[1, 194, 8, 64], [193, 2, 248, 64], [1, 210, 8, 320], [1, 2, 136, 64]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 48, 'inner_split': False, 'inner_tex': 'C_6:D_4', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 44], [4, 12]], 'label': '384.2088', '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': '(C2^2*C6).D8', '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': 27, 'number_characteristic_subgroups': 39, 'number_conjugacy_classes': 72, 'number_divisions': 48, 'number_normal_subgroups': 125, 'number_subgroup_autclasses': 168, 'number_subgroup_classes': 336, 'number_subgroups': 894, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 15], [3, 2], [4, 144], [6, 30], [8, 96], [12, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 2, 2, 4, 4, 2], 'outer_gen_pows': [273, 0, 16, 0, 0, 128, 16], 'outer_gens': [[193, 211, 72, 64], [225, 51, 316, 320], [33, 195, 56, 320], [229, 6, 40, 64], [37, 23, 56, 64], [197, 39, 72, 64], [5, 54, 72, 320]], 'outer_group': '512.10493082', 'outer_hash': 7367214181469736260, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [382582214846963831172641076849797072064525715062251103108853209350661423724718894764958249956927770503238060275999509805023618750095130294866874852717828951134903574461006888591339391706040041860775760028236555759902, 76563215997124184075323185930912358975941604532537134700526591683602916658502348306319726858262822358025174413537262817356462372547992178096690016108425941719790733126528657661258397946179104792693788559242941954633, 124837372576427774555106056843252683648927643557018598854295029748856252553707517570180384295935674532188044470704101617020355468535501093853738446645441263514828542206175548786099764312017564636758715116010777023024, 318898775168715381720681964360581225703658251705042836489710001663859678290269521792305299788851174587243640535235907700513496073318320615762191093727036541857305451544206133598974473611573166913172113982128406454428, 296773514969019566701504223065060553820720138468962908960592330251400826551239608518746486214790227824379791836609376645569110675704878698896858691308707889013726334218530870624373919528394648139746896092388461681802, 46602019000395481666226718460980535001443931155818281052482354850624647265856687776908671747754121902797352847012967632342242215561445578771522034819703470566152227031212368586344120410255975662961332275280745844808, 201251436988026490032716809825698861012223682601935468514410872627212570749188743254604920984874381974967976312132757788133647601699334192868069506277664168167880156760826341737693396024663379594229380587029651941184], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 20], [8, 4]], 'representations': {'PC': {'code': 4180357620400050555757528206072321, 'gens': [1, 2, 4, 7], 'pres': [8, -2, -2, -2, -2, -2, -2, -2, -3, 3105, 41, 3979, 91, 972, 116, 2270, 166, 2079]}, 'GLZN': {'d': 2, 'p': 48, 'gens': [111169, 2764825, 111361, 111745, 1315165, 774151, 2171965, 2821273]}, 'Perm': {'d': 19, 'gens': [6446835113247651, 12914592058743196, 20713823523996643, 27414266513356800, 18498, 12316, 20713823523993600, 3991680]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2^2\\times C_6).D_8', 'transitive_degree': 192, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 4], 'aut_gens': [[1, 4], [1, 6], [1, 12], [3, 4], [5, 4]], 'aut_group': '32.27', 'aut_hash': 27, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 32, 'aut_permdeg': 8, 'aut_perms': [10880, 16328, 12316, 6781], 'aut_phi_ratio': 4.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 2, 1], [4, 2, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^2\\wr C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [4, 2, 6]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [4, 2, 1, 2], [4, 2, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [4], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '4.2', 'hash': 4, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 12], [9, 4]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 2]], 'label': '16.4', 'linC_count': 8, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 5, 'linQ_dim': 4, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4:C4', 'ngens': 2, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 10, 'number_divisions': 8, 'number_normal_subgroups': 11, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 13, 'number_subgroups': 15, 'old_label': None, 'order': 16, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 3], [4, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [4, 0], 'outer_gens': [[5, 4], [7, 6]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [7, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 8, 'pgroup': 2, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4]], 'representations': {'PC': {'code': 141333, 'gens': [1, 3], 'pres': [4, 2, 2, 2, 2, 8, 146, 34]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7233580, 26129426]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1816751, 1282502, 438254, 1565004]}, 'Perm': {'d': 8, 'gens': [1569, 5896, 11520, 16]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4:C_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
