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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '480.719', 'ambient_counter': 719, 'ambient_order': 480, 'ambient_tex': '(C_2\\times C_{20}):C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': True, 'core_order': 480, 'counter': 1, 'cyclic': False, 'direct': True, 'hall': 30, 'label': '480.719.1.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '1.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': False, 'quotient': '1.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 1, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_1', 'simple': False, 'solvable': True, 'special_labels': ['R', 'L0', 'D0', 'C0'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.719', 'subgroup_hash': 719, 'subgroup_order': 480, 'subgroup_tex': '(C_2\\times C_{20}):C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '480.719', 'aut_centralizer_order': None, 'aut_label': '1.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '20.b1.a1', 'complements': ['480.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': [], 'contains': ['2.a1.a1', '2.b1.a1', '2.b1.b1', '2.c1.a1', '2.c1.b1', '2.d1.a1', '2.d1.b1', '3.a1.a1', '5.a1.a1'], 'core': '1.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [2925, 6652, 7485, 8015, 3063, 2495, 7218, 7215], 'generators': [1, 8, 240, 320, 4, 96, 2], 'label': '480.719.1.a1.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '1.a1.a1', 'normal_contained_in': [], 'normal_contains': ['2.a1.a1', '2.b1.b1', '2.b1.a1', '2.c1.a1', '2.c1.b1', '2.d1.b1', '2.d1.a1', '3.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '1.a1.a1', 'projective_image': '20.4', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1.a1.a1', 'subgroup_fusion': None, 'weyl_group': '20.4'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [20, 2, 4, 4, 4, 4, 20], 'aut_gens': [[1, 4, 16], [439, 6, 184], [1, 6, 306], [109, 12, 314], [391, 4, 368], [351, 14, 274], [295, 12, 306], [341, 6, 178]], 'aut_group': None, 'aut_hash': 592289769436509937, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10240, 'aut_permdeg': 82, 'aut_perms': [353520370047801246667139852640688924337731234668939932110456056465763669138960520493498067415613495217856844430668783643996, 121853852398313126196608385462022913733112353254298281778514711463526851001553087832493774019646710788194116584340745306071, 104025486764804064800479526333983242167691484922778375654651872171279235472441538356373165794907063415092258222545815105973, 462194294775068471287255526325987212426406909675553114338247573045983084897646185189121737262970982372979035902113857579321, 149469572512140742583734919105778635246121963113404673265725207106893998815204638577576900430680398439235559354675632521764, 339086701377149608142469621771933315968831952740074654304193598734491976548120654513996353018630406302521180778042871272622, 194900876402477051972064035241524611417961510724911483781852351876655063540711136775903724129345701965515174250753517392235], 'aut_phi_ratio': 80.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [4, 2, 2, 1], [4, 10, 8, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 4, 1], [10, 2, 2, 1], [10, 2, 4, 1], [10, 2, 8, 1], [12, 1, 8, 1], [12, 2, 4, 1], [12, 10, 16, 1], [15, 2, 4, 1], [20, 2, 8, 2], [30, 2, 4, 1], [30, 2, 8, 1], [30, 2, 16, 1], [60, 2, 16, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_5:(C_2\\times C_4\\times C_2^6.C_2^2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '256.29598', 'autcent_hash': 29598, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '40.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 40, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 1, 2], [4, 1, 4], [4, 2, 2], [4, 10, 8], [5, 2, 2], [6, 1, 6], [6, 2, 4], [10, 2, 14], [12, 1, 8], [12, 2, 4], [12, 10, 16], [15, 2, 4], [20, 2, 16], [30, 2, 28], [60, 2, 32]], 'center_label': '24.9', 'center_order': 24, 'central_product': True, 'central_quotient': '20.4', 'commutator_count': 1, 'commutator_label': '10.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 719, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['160.147', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 1, 2, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 10, 2, 4], [5, 2, 2, 1], [6, 1, 2, 3], [6, 2, 2, 2], [10, 2, 2, 3], [10, 2, 4, 2], [12, 1, 4, 2], [12, 2, 2, 2], [12, 10, 4, 4], [15, 2, 4, 1], [20, 2, 4, 4], [30, 2, 4, 3], [30, 2, 8, 2], [60, 2, 8, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3276, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.44', 'hash': 719, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 1, 10], 'inner_gens': [[1, 4, 312], [1, 4, 16], [201, 4, 16]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 20, 'inner_split': False, 'inner_tex': 'D_{10}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 108]], 'label': '480.719', 'linC_count': 1024, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 64, 'linQ_dim': 12, 'linQ_dim_count': 296, 'linR_count': 256, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2*C20):C12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 156, 'number_divisions': 48, 'number_normal_subgroups': 98, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 152, 'number_subgroups': 336, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 88], [5, 4], [6, 14], [10, 28], [12, 176], [15, 8], [20, 32], [30, 56], [60, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 4, 4, 4, 2], 'outer_gen_pows': [384, 0, 0, 0, 0, 0, 16], 'outer_gens': [[439, 6, 184], [1, 6, 306], [109, 12, 314], [391, 4, 368], [351, 14, 274], [295, 12, 306], [341, 6, 178]], 'outer_group': '512.7535015', 'outer_hash': 1502494614874769598, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [3157085713757746723819588536042171847952431199821261705012745903994073461279117362195725994700877034427787387429611824683630904029232754202771156012649808559255434775982938476106416786211893969739169495157403108163, 2284843884442286429737155675030139126131620936367499077592943336871388568700480968629619605163255608171774396147082091258682232596313243383000210064521845956820274392550285023940076916468930084600930492148888944, 6193847022633929690055466387266904952014218515194815821423844902271413088819257409473798223000576414074681801220147354173719103549135788544415121045194992198177351981487257199770411035725795568795107187964535014565, 9230409524750250863060166381143649148969960236048739224014799404525795736734662585554683787533261028726196518200662830099250478202872876756194008751194378447520617836310926780884914950470693167064780244357333181642, 12266988458834895782976404336485943949519911795920557605047293058317903571088339328571866789954093001355520763083839866887452975142179013217491439790969866482145931630698119463273080306714354365970106347634580603066, 15301677438439720485383528550672733113727596561430460445555225797120123346295225799336964968797158974226495588280574062008801474263264643618591796797096667305990765704559167637256846803385166009080918099779081888293, 18339943386443978198119700260780371771736041962971819100405240740490346492799751107989990492877898420451255147548475681206039153502284957758751184656607193620097593660602435356228420549618668928630100093949018272415], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4.C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 14], [8, 10], [16, 2], [32, 2]], 'representations': {'PC': {'code': 80745943008266323645009051655, 'gens': [1, 3, 5], 'pres': [7, -2, -2, -2, -2, 2, -3, -5, 14, 58, 10924, 102, 5381, 166, 18822]}, 'GLZN': {'d': 2, 'p': 65, 'gens': [275471, 14005926, 4394016, 3844764, 5767146, 12316234, 7417513]}, 'Perm': {'d': 20, 'gens': [1447769925867624, 135205689832012800, 262560264661094400, 3, 87091200, 391971468784896000, 6504]}}, 'schur_multiplier': [2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_{20}):C_{12}', 'transitive_degree': 240, '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': '48.44', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [20, 2, 4, 4, 4, 4, 20], 'aut_gens': [[1, 4, 16], [439, 6, 184], [1, 6, 306], [109, 12, 314], [391, 4, 368], [351, 14, 274], [295, 12, 306], [341, 6, 178]], 'aut_group': None, 'aut_hash': 592289769436509937, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10240, 'aut_permdeg': 82, 'aut_perms': [353520370047801246667139852640688924337731234668939932110456056465763669138960520493498067415613495217856844430668783643996, 121853852398313126196608385462022913733112353254298281778514711463526851001553087832493774019646710788194116584340745306071, 104025486764804064800479526333983242167691484922778375654651872171279235472441538356373165794907063415092258222545815105973, 462194294775068471287255526325987212426406909675553114338247573045983084897646185189121737262970982372979035902113857579321, 149469572512140742583734919105778635246121963113404673265725207106893998815204638577576900430680398439235559354675632521764, 339086701377149608142469621771933315968831952740074654304193598734491976548120654513996353018630406302521180778042871272622, 194900876402477051972064035241524611417961510724911483781852351876655063540711136775903724129345701965515174250753517392235], 'aut_phi_ratio': 80.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [4, 2, 2, 1], [4, 10, 8, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 4, 1], [10, 2, 2, 1], [10, 2, 4, 1], [10, 2, 8, 1], [12, 1, 8, 1], [12, 2, 4, 1], [12, 10, 16, 1], [15, 2, 4, 1], [20, 2, 8, 2], [30, 2, 4, 1], [30, 2, 8, 1], [30, 2, 16, 1], [60, 2, 16, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_5:(C_2\\times C_4\\times C_2^6.C_2^2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '256.29598', 'autcent_hash': 29598, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5:D_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '40.12', 'autcentquo_hash': 12, 'autcentquo_nilpotent': False, 'autcentquo_order': 40, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 1, 2], [4, 1, 4], [4, 2, 2], [4, 10, 8], [5, 2, 2], [6, 1, 6], [6, 2, 4], [10, 2, 14], [12, 1, 8], [12, 2, 4], [12, 10, 16], [15, 2, 4], [20, 2, 16], [30, 2, 28], [60, 2, 32]], 'center_label': '24.9', 'center_order': 24, 'central_product': True, 'central_quotient': '20.4', 'commutator_count': 1, 'commutator_label': '10.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 719, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['160.147', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 1, 2, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 10, 2, 4], [5, 2, 2, 1], [6, 1, 2, 3], [6, 2, 2, 2], [10, 2, 2, 3], [10, 2, 4, 2], [12, 1, 4, 2], [12, 2, 2, 2], [12, 10, 4, 4], [15, 2, 4, 1], [20, 2, 4, 4], [30, 2, 4, 3], [30, 2, 8, 2], [60, 2, 8, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3276, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.44', 'hash': 719, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 10, 'inner_gen_orders': [2, 1, 10], 'inner_gens': [[1, 4, 312], [1, 4, 16], [201, 4, 16]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 20, 'inner_split': False, 'inner_tex': 'D_{10}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 108]], 'label': '480.719', 'linC_count': 1024, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 64, 'linQ_dim': 12, 'linQ_dim_count': 296, 'linR_count': 256, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': '(C2*C20):C12', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 156, 'number_divisions': 48, 'number_normal_subgroups': 98, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 152, 'number_subgroups': 336, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 88], [5, 4], [6, 14], [10, 28], [12, 176], [15, 8], [20, 32], [30, 56], [60, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 4, 4, 4, 4, 2], 'outer_gen_pows': [384, 0, 0, 0, 0, 0, 16], 'outer_gens': [[439, 6, 184], [1, 6, 306], [109, 12, 314], [391, 4, 368], [351, 14, 274], [295, 12, 306], [341, 6, 178]], 'outer_group': '512.7535015', 'outer_hash': 1502494614874769598, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [3157085713757746723819588536042171847952431199821261705012745903994073461279117362195725994700877034427787387429611824683630904029232754202771156012649808559255434775982938476106416786211893969739169495157403108163, 2284843884442286429737155675030139126131620936367499077592943336871388568700480968629619605163255608171774396147082091258682232596313243383000210064521845956820274392550285023940076916468930084600930492148888944, 6193847022633929690055466387266904952014218515194815821423844902271413088819257409473798223000576414074681801220147354173719103549135788544415121045194992198177351981487257199770411035725795568795107187964535014565, 9230409524750250863060166381143649148969960236048739224014799404525795736734662585554683787533261028726196518200662830099250478202872876756194008751194378447520617836310926780884914950470693167064780244357333181642, 12266988458834895782976404336485943949519911795920557605047293058317903571088339328571866789954093001355520763083839866887452975142179013217491439790969866482145931630698119463273080306714354365970106347634580603066, 15301677438439720485383528550672733113727596561430460445555225797120123346295225799336964968797158974226495588280574062008801474263264643618591796797096667305990765704559167637256846803385166009080918099779081888293, 18339943386443978198119700260780371771736041962971819100405240740490346492799751107989990492877898420451255147548475681206039153502284957758751184656607193620097593660602435356228420549618668928630100093949018272415], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4.C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 14], [8, 10], [16, 2], [32, 2]], 'representations': {'PC': {'code': 80745943008266323645009051655, 'gens': [1, 3, 5], 'pres': [7, -2, -2, -2, -2, 2, -3, -5, 14, 58, 10924, 102, 5381, 166, 18822]}, 'GLZN': {'d': 2, 'p': 65, 'gens': [275471, 14005926, 4394016, 3844764, 5767146, 12316234, 7417513]}, 'Perm': {'d': 20, 'gens': [1447769925867624, 135205689832012800, 262560264661094400, 3, 87091200, 391971468784896000, 6504]}}, 'schur_multiplier': [2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_{20}):C_{12}', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 1]], '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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, 'wreath_data': None, 'wreath_product': False}
