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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '448.759', 'ambient_counter': 759, 'ambient_order': 448, 'ambient_tex': '(Q_8\\times C_{14}):C_4', 'central': True, 'central_factor': False, 'centralizer_order': 448, 'characteristic': False, 'core_order': 2, 'counter': 145, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '448.759.224.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '224.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '224.137', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 137, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 224, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{28}.D_4', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '448.759', 'aut_centralizer_order': None, 'aut_label': '224.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['32.a1.a1', '112.a1.a1', '112.f1.a1', '112.g1.a1'], 'contains': ['448.a1.a1'], 'core': '224.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [4], 'label': '448.759.224.a1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '224.a1.a1', 'normal_contained_in': ['32.a1.a1', '112.a1.a1'], 'normal_contains': ['448.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '224.a1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '224.a1.a1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', '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': [[1]], '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], [2, 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], [2, 1, 1]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': 84, 'aut_gen_orders': [12, 4, 2, 4, 6, 4, 6, 6], 'aut_gens': [[1, 2, 8, 32], [253, 374, 8, 96], [229, 222, 8, 432], [17, 14, 24, 436], [21, 234, 24, 416], [229, 106, 8, 176], [29, 366, 8, 436], [1, 54, 8, 112], [9, 54, 24, 368]], 'aut_group': None, 'aut_hash': 7915036427112127641, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 43008, 'aut_permdeg': 128, 'aut_perms': [74575411180885245811801399003263490480225103260317739684401294981806857113767796595123982857454364204415708790069260392351027935918770387789879864066377558111047769466063649188878618186931007237567804905470447935333, 127282837398081409117425932318524705479918034538955893998717210935409313720769020709681698206558438823094609126973152085548142128808932994574878449828675626450334300397424743397904711437811687378623999265248119985589, 49522776520550910485094416457502469428164678560108440738381784637303678650862808348968630440420078175581820438845634276675155385080736902615407464126873788737636940016507539141201872056255254812760851468523312059738, 150828551855284978311381984735868858836331317427891117391072165030165442068458608275941580162306104198925623267867006123873859409774405158419556377932418899587709564985559613973616020853993043773570276229866908481023, 235738574539770986038324378754648792286049583827435432671934631858953518300469929841863655312273417308522964747195530131429733675827814546294166254526975195172004688774881861013946061380370641872371175348436665370079, 232499353989086101169274875766971275195692131625238135461228682742403742757677487080827550353323534595140771400977684936938235115632920356384082122559546393734999221059170872706393326888472272874634992495991253271501, 370595187611593185234211110393294860896989384939863232352103143303362759587514693013441194377260428134422123537544148873680680751538377261204167579909179925500691386087254566994527138219455794547185071650786761406175, 78701633628650291055698325782996173391851490058169306286244225580721897045714538155800952641955537026595130682962303348963545849899232584448467459262768113151961262627652889136538992001903792033243372992134219844031], 'aut_phi_ratio': 224.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 4, 4, 1], [4, 28, 4, 1], [7, 2, 3, 1], [8, 28, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 2, 12, 1], [28, 4, 3, 2], [28, 4, 6, 1], [28, 4, 24, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_7.(C_2^4\\times C_6).C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '672.1266', 'autcentquo_hash': 1266, 'autcentquo_nilpotent': False, 'autcentquo_order': 672, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [4, 2, 4], [4, 4, 4], [4, 28, 4], [7, 2, 3], [8, 28, 4], [14, 2, 21], [28, 4, 36]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '112.36', 'commutator_count': 1, 'commutator_label': '28.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 759, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [4, 2, 1, 4], [4, 4, 1, 4], [4, 28, 2, 2], [7, 2, 3, 1], [8, 28, 2, 2], [14, 2, 3, 3], [14, 2, 6, 2], [28, 4, 3, 4], [28, 4, 6, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 672, 'exponent': 56, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '56.12', 'hash': 759, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 2, 2, 14], 'inner_gens': [[1, 26, 24, 32], [9, 2, 24, 432], [17, 18, 8, 32], [1, 82, 8, 32]], 'inner_hash': 36, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': False, 'inner_tex': 'C_{14}:D_4', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 52], [4, 14]], 'label': '448.759', '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': '(Q8*C14):C4', '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': 18, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 82, 'number_divisions': 32, 'number_normal_subgroups': 71, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 150, 'number_subgroups': 436, 'old_label': None, 'order': 448, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [4, 136], [7, 6], [8, 112], [14, 42], [28, 144]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 2, 12], 'outer_gen_pows': [0, 0, 232, 0, 0, 0], 'outer_gens': [[225, 226, 24, 32], [1, 2, 8, 48], [21, 246, 8, 48], [25, 2, 24, 32], [1, 6, 8, 48], [225, 226, 24, 372]], 'outer_group': '384.19891', 'outer_hash': 19891, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [83502720, 744, 124104960, 88216170000, 193158120960, 456978412803], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6:C_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 2], [6, 8], [12, 4], [24, 2]], 'representations': {'PC': {'code': 307559531994839193287549782954249349, 'gens': [1, 2, 4, 6], 'pres': [7, -2, -2, -2, -2, -2, 2, -7, 112, 365, 36, 675, 346, 80, 9084, 124, 9421]}, 'Perm': {'d': 27, 'gens': [452493885619591169876489649, 886210513628923025493350400, 1307371708261960212595046416, 1724458845663626373579801616, 2094169701829910578704230400, 1724458845663626373579801600, 4364760]}}, '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': '(Q_8\\times C_{14}):C_4', 'transitive_degree': 224, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [2, 2, 2, 12, 28], 'aut_gens': [[1, 2, 8], [113, 2, 120], [169, 170, 216], [1, 6, 8], [5, 2, 200], [169, 218, 8]], 'aut_group': '2688.dt', 'aut_hash': 8551432399099159210, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2688, 'aut_permdeg': 15, 'aut_perms': [7983360, 87660922138, 479001600, 187293295155, 8025699], 'aut_phi_ratio': 28.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 28, 1, 1], [4, 2, 1, 2], [4, 4, 2, 1], [4, 28, 1, 1], [7, 2, 3, 1], [8, 28, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [28, 4, 3, 2], [28, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_7\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '336.216', 'autcentquo_hash': 216, 'autcentquo_nilpotent': False, 'autcentquo_order': 336, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 28, 1], [4, 2, 2], [4, 4, 2], [4, 28, 1], [7, 2, 3], [8, 28, 2], [14, 2, 9], [28, 4, 18]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '112.36', 'commutator_count': 1, 'commutator_label': '28.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 137, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 28, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 28, 1, 1], [7, 2, 3, 1], [8, 28, 1, 2], [14, 2, 3, 1], [14, 2, 6, 1], [28, 4, 3, 2], [28, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 56, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[4, 0, 6]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '56.12', 'hash': 137, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 28, 'inner_gen_orders': [2, 4, 14], 'inner_gens': [[1, 6, 120], [117, 2, 216], [113, 18, 8]], 'inner_hash': 36, 'inner_nilpotent': False, 'inner_order': 112, 'inner_split': True, 'inner_tex': 'C_{14}:D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 24, 'irrQ_dim': 48, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 26], [4, 7]], 'label': '224.137', 'linC_count': 6, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 14, 'linQ_dim_count': 4, 'linR_count': 3, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.D4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 15, 'number_characteristic_subgroups': 19, 'number_conjugacy_classes': 41, 'number_divisions': 18, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 60, 'number_subgroups': 222, 'old_label': None, 'order': 224, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 31], [4, 40], [7, 6], [8, 56], [14, 18], [28, 72]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 4, 56], 'outer_gens': [[1, 2, 120], [5, 2, 120], [57, 58, 72]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [744, 24, 40323], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 23, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 1], [6, 4], [12, 2], [24, 1]], 'representations': {'PC': {'code': 78216869837291616702289465541102021, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, -2, -2, -7, 672, 73, 31, 2090, 518, 2883, 2601, 69, 3130, 88, 3467]}, 'Perm': {'d': 23, 'gens': [1134643256731346786047, 2514161715068303596800, 3696112211801025542400, 4752207122534610681600, 5988479609728376046720, 973]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{28}.D_4', 'transitive_degree': 112, 'wreath_data': None, 'wreath_product': False}
