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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.4656', 'ambient_counter': 4656, 'ambient_order': 960, 'ambient_tex': 'C_2\\times C_{30}.D_8', 'central': False, 'central_factor': True, 'centralizer_order': 40, 'characteristic': True, 'core_order': 192, 'counter': 25, 'cyclic': False, 'direct': True, 'hall': 6, 'label': '960.4656.5.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '192.521', 'subgroup_hash': 521, 'subgroup_order': 192, 'subgroup_tex': 'C_2\\times C_6.D_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.4656', 'aut_centralizer_order': None, 'aut_label': '5.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '24.a1.a1', 'complements': ['192.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '10.d1.a1', '10.d1.b1', '10.d1.c1', '10.d1.d1', '15.a1.a1'], 'core': '5.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [1, 16, 24, 4, 640, 480, 2], 'label': '960.4656.5.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '5.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['10.a1.a1', '10.b1.a1', '10.c1.a1', '10.d1.d1', '10.d1.c1', '10.d1.b1', '10.d1.a1'], 'normalizer': '1.a1.a1', 'old_label': '5.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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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, 4, 6, 6, 12, 4, 4, 4], 'aut_gens': [[1, 4, 32], [123, 14, 160], [27, 132, 162], [17, 70, 50], [9, 172, 32], [27, 52, 50], [97, 86, 162], [113, 84, 178], [105, 100, 48]], 'aut_group': None, 'aut_hash': 7418388897072767239, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 64, 'aut_perms': [110770175956049844169095027425420502736043986396398877777308680650418346614661624601646032, 70478291201775589682078047535269225931300368106966656495319531490478053263442401563031632, 1983119029833309779077191270545020015872248123596537825935718198183202663442245336766727, 64467015942637931133055271156370362741332764999243720962193716623904895385117620809395200, 70478288523620702591266535452298108057320476182408913793489829988576212293755068884980472, 40291887013741967769148334954528740690473199940797520546664194636989265673478093790555503, 42275002622507905270042969614809560309257224972254577158553103039503620546803148675612792, 104758901858389683085883658055892565806031897081996564196808171037847581355616169969408007], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 4, 1], [4, 12, 4, 1], [6, 2, 1, 3], [6, 2, 4, 1], [8, 6, 8, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^4.C_2^6.C_2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 8935, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5.C_2^3', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 24, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 12, 4], [6, 2, 7], [8, 6, 8], [12, 4, 12]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 521, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['96.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 2, 1, 1], [4, 2, 1, 4], [4, 4, 2, 2], [4, 12, 2, 2], [6, 2, 1, 7], [8, 6, 2, 4], [12, 4, 1, 4], [12, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 336, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '24.14', 'hash': 521, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 28, 32], [9, 4, 160], [1, 68, 32]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': None, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 28], [4, 4]], 'label': '192.521', '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*C6.D8', 'ngens': 7, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 20, 'number_characteristic_subgroups': 27, 'number_conjugacy_classes': 48, 'number_divisions': 34, 'number_normal_subgroups': 79, 'number_subgroup_autclasses': 76, 'number_subgroup_classes': 130, 'number_subgroups': 280, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 72], [6, 14], [8, 48], [12, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 2, 2, 4, 4, 2], 'outer_gen_pows': [0, 0, 8, 0, 0, 0], 'outer_gens': [[113, 116, 48], [3, 20, 34], [123, 22, 32], [123, 20, 34], [105, 116, 50], [3, 6, 50]], 'outer_group': '256.27633', 'outer_hash': 27633, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 64, 'outer_perms': [26011252978399261675953902021061588442772975550119807376348924859276518811952608875055536, 65935651125508663328369840463031381655240160101794471304629129441127254997461065509779084, 25897425495503924812760020035388470700834290541713486715071664333644877827482520, 99016711711540305397307243537425981124543287378218781173949766387258531434711155958681177, 56923452161139267884395536545927248703151239668884745647875948019849638701861800847255378, 99016711737651741236724103285965262800073496692196095940131776475654314587602131799237059], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5:D_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 14]], 'representations': {'PC': {'code': 166993666269766018098321025, 'gens': [1, 3, 6], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 14, 590, 58, 675, 80, 1699, 124, 1588]}, 'GLZN': {'d': 2, 'p': 40, 'gens': [109009, 64401, 576009, 77793, 64801, 1344021, 2369027]}, 'Perm': {'d': 17, 'gens': [23725950796920, 45787363816320, 21122138056329, 16, 68361751180800, 45787363776000, 840]}}, 'schur_multiplier': [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\\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': '80.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 4, 12, 4, 4, 12, 12, 12], 'aut_gens': [[1, 4, 32], [481, 164, 354], [17, 340, 752], [489, 6, 370], [489, 190, 624], [25, 182, 354], [505, 492, 240], [497, 188, 34], [497, 812, 48], [507, 180, 242]], 'aut_group': None, 'aut_hash': 7714637356874725850, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 68, 'aut_perms': [742973484890006729131960506157445022987864351060347017852721123833349405385454465591619067629546, 1110964534086740907442082273593628335057163012655776361989119785825462546622194123114577895866352, 936099832311306409691809023897268461842067606267982292961040131095092684362624026274128148421411, 922890045500578578366959552748377866111214682681418424595726504668961742580849161579407551226898, 1131024067047135920069000847617491084733799700585496751480807799315560686032202347768857269288276, 1739156889202860984848129528994232755482617324124522637829542880479822182031897780239611763195038, 1654932123801562553514719552260801399844436618773835439683652318997994775574086681795128023226585, 1654902610487106582660597071970146636820010990601969967354767123261310915632525274686027058170979, 2169868347734496613352062210564749374560829513304650278874352063362167448465786285089883189011736], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [3, 2, 1, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 4, 1], [4, 12, 4, 1], [5, 1, 4, 1], [6, 2, 1, 3], [6, 2, 4, 1], [8, 6, 8, 1], [10, 1, 4, 3], [10, 1, 16, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 4, 8, 1], [15, 2, 4, 1], [20, 2, 4, 2], [20, 2, 8, 1], [20, 4, 16, 1], [20, 12, 16, 1], [30, 2, 4, 3], [30, 2, 16, 1], [40, 6, 32, 1], [60, 4, 4, 2], [60, 4, 8, 1], [60, 4, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^5.C_2^6.C_2^2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 7177616586376182635, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5.C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 2, 1], [4, 2, 4], [4, 4, 4], [4, 12, 4], [5, 1, 4], [6, 2, 7], [8, 6, 8], [10, 1, 28], [12, 4, 12], [15, 2, 4], [20, 2, 16], [20, 4, 16], [20, 12, 16], [30, 2, 28], [40, 6, 32], [60, 4, 48]], 'center_label': '40.14', 'center_order': 40, 'central_product': True, 'central_quotient': '24.8', 'commutator_count': 1, 'commutator_label': '12.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4656, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1], ['96.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 2, 1, 1], [4, 2, 1, 4], [4, 4, 2, 2], [4, 12, 2, 2], [5, 1, 4, 1], [6, 2, 1, 7], [8, 6, 2, 4], [10, 1, 4, 7], [12, 4, 1, 4], [12, 4, 4, 2], [15, 2, 4, 1], [20, 2, 4, 4], [20, 4, 8, 2], [20, 12, 8, 2], [30, 2, 4, 7], [40, 6, 8, 4], [60, 4, 4, 4], [60, 4, 16, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 10416, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.45', 'hash': 4656, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 4, 3], 'inner_gens': [[1, 28, 32], [9, 4, 352], [1, 644, 32]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': True, 'inner_tex': 'C_3:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 80], [2, 140], [4, 20]], 'label': '960.4656', '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*C30.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, 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': 54, 'number_conjugacy_classes': 240, 'number_divisions': 68, 'number_normal_subgroups': 158, 'number_subgroup_autclasses': 152, 'number_subgroup_classes': 260, 'number_subgroups': 560, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 72], [5, 4], [6, 14], [8, 48], [10, 28], [12, 48], [15, 8], [20, 288], [30, 56], [40, 192], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 4, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 8, 8], 'outer_gens': [[505, 22, 626], [507, 6, 242], [3, 500, 242], [25, 6, 226], [25, 502, 226], [25, 20, 626], [25, 4, 626]], 'outer_group': None, 'outer_hash': 9087809238134369064, 'outer_nilpotent': True, 'outer_order': 1024, 'outer_permdeg': 18, 'outer_perms': [127382520, 377917979459767, 377924246380936, 1067062411663921, 377917979806222, 753220523064240, 753220523064247], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6.C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [4, 22], [8, 12], [16, 14]], 'representations': {'PC': {'code': 13014065602267708714086920924598954164231, 'gens': [1, 3, 6], 'pres': [8, -2, -2, -2, -2, -2, -2, -3, -5, 16, 674, 66, 771, 91, 4245, 141, 9878, 222]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [15673879, 683409, 806761, 2233789, 6133257, 685345, 49875609, 44295745]}, 'Perm': {'d': 22, 'gens': [53780336661602074320, 3669840, 51597817679544151680, 33, 3669120, 109750244591699712000, 163613728419837696000, 6706022400]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 20], '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_{30}.D_8', 'transitive_degree': 960, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [2]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_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], [5, 1, 4]], 'center_label': '5.1', 'center_order': 5, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['5.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 1, 'exponent': 5, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5.1', 'hash': 1, 'hyperelementary': 5, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 5]], 'label': '5.1', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 5, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 5, 'order_factorization_type': 1, 'order_stats': [[1, 1], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 5, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -5]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26329372]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131]}, 'Perm': {'d': 5, 'gens': [96]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [5], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5', 'transitive_degree': 5, 'wreath_data': None, 'wreath_product': False}
