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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '672.607', 'ambient_counter': 607, 'ambient_order': 672, 'ambient_tex': 'C_{84}:D_4', 'central': True, 'central_factor': False, 'centralizer_order': 672, 'characteristic': False, 'core_order': 2, 'counter': 92, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '672.607.336.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '336.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '336.150', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 150, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 336, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{14}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, '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': '672.607', 'aut_centralizer_order': 32256, 'aut_label': '336.a1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '1.1', 'aut_weyl_index': 64512, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['48.a1', '112.a1', '168.a1', '168.c1', '168.d1', '168.e1'], 'contains': ['672.a1'], 'core': '336.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [2132, 2742, 2123, 4440], 'generators': [4], 'label': '672.607.336.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '336.a1', 'normal_contained_in': ['48.a1', '112.a1', '168.a1'], 'normal_contains': ['672.a1'], 'normalizer': '1.a1', 'old_label': '336.a1', 'projective_image': '336.150', 'quotient_action_image': '1.1', 'quotient_action_kernel': '336.150', 'quotient_action_kernel_order': 336, 'quotient_fusion': None, 'short_label': '336.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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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': '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': [12, 12, 6, 4, 12, 12, 12], 'aut_gens': [[1, 2, 8], [229, 250, 140], [281, 526, 476], [5, 390, 524], [57, 518, 328], [117, 186, 632], [397, 470, 540], [509, 270, 44]], 'aut_group': None, 'aut_hash': 8662371451100837692, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 80, 'aut_perms': [54991127015947598072199235194237807341454220569437764241318737318453781865986395970177200661194025021835360744864072438, 70732383887197040909967206206344508446431437800322191271532161162118570815239251788668134164996800434493454119754684326, 66113070948487772365902339592319895449480714115598026527325361990117247115978152893589479105008546828730628530738480101, 7244147790166916187553229737131773092722976519133366434225237190932676528113902840785108567777607926731148712366932266, 18402650055138329204715322384875408852793757214900421617346488926147744767226191230242102854460827307048966136748163219, 3793725712808252165037322962788555123459285016899652844466970265146315935476247239304444045260309107687710516366488168, 35375508814482303761494976950778618531119417702007793118108123593477844382677350708351321982987040247607054477350638243], 'aut_phi_ratio': 336.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 12, 2, 1], [2, 28, 2, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 42, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 28, 4, 1], [7, 2, 3, 1], [12, 4, 2, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 12, 12, 1], [21, 4, 3, 1], [28, 4, 6, 1], [42, 4, 3, 1], [42, 4, 6, 1], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '1008.906', 'autcentquo_hash': 906, 'autcentquo_nilpotent': False, 'autcentquo_order': 1008, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 12, 2], [2, 28, 2], [3, 2, 1], [4, 2, 2], [4, 42, 4], [6, 2, 3], [6, 28, 4], [7, 2, 3], [12, 4, 2], [14, 2, 9], [14, 12, 12], [21, 4, 3], [28, 4, 6], [42, 4, 9], [84, 4, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '168.50', 'commutator_count': 2, 'commutator_label': '84.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 607, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 12, 1, 2], [2, 28, 1, 2], [3, 2, 1, 1], [4, 2, 1, 2], [4, 42, 1, 4], [6, 2, 1, 3], [6, 28, 2, 2], [7, 2, 3, 1], [12, 4, 1, 2], [14, 2, 3, 3], [14, 12, 6, 2], [21, 4, 3, 1], [28, 4, 3, 2], [42, 4, 3, 3], [84, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1344, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '168.50', 'hash': 607, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 42], 'inner_gens': [[1, 6, 568], [5, 2, 328], [113, 354, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': False, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 8], [2, 38], [4, 32]], 'label': '672.607', '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': 'C84:D4', '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': 21, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 78, 'number_divisions': 36, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 216, 'number_subgroups': 1576, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 83], [3, 2], [4, 172], [6, 118], [7, 6], [12, 8], [14, 162], [21, 12], [28, 24], [42, 36], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 4, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 344], [1, 2, 236], [169, 2, 348], [169, 170, 232], [1, 338, 488]], 'outer_group': '384.16843', 'outer_hash': 16843, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [39844991760, 33617930520, 6227061984, 200749571304, 469592123283], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6.D_4^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 4], [6, 4], [12, 8], [24, 2]], 'representations': {'PC': {'code': 2380025127455168313067702990210481733681258251, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 85, 36, 15907, 4602, 80, 16244, 11491, 102, 10757, 13452, 166, 14125]}, 'GLZN': {'d': 2, 'p': 84, 'gens': [593713, 1089227, 42082055, 1042546, 593363, 17188445, 17588257]}, 'Perm': {'d': 18, 'gens': [21010447947624, 3670801, 960, 7983360, 2424, 3, 397707843456000]}}, 'schur_multiplier': [2, 2, 4], '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_{84}:D_4', 'transitive_degree': 336, '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': [6, 6, 2, 6, 12, 6], 'aut_gens': [[1, 2, 4], [113, 26, 220], [113, 122, 188], [1, 242, 52], [169, 194, 20], [85, 62, 292], [113, 26, 316]], 'aut_group': None, 'aut_hash': 866793471638122205, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4032, 'aut_permdeg': 40, 'aut_perms': [789855141415794589778252682930450910739274810062, 436813588547839158645466491701698297391128904702, 347301541702267840016912040832880607335277265577, 782381398565310980360206479090303566265159294177, 689711259792608704055878482205652471805548889053, 789854950977745275318728900582154638304066377250], 'aut_phi_ratio': 42.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 2, 1], [2, 14, 2, 1], [2, 21, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [6, 2, 1, 1], [6, 28, 2, 1], [7, 2, 3, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 12, 6, 1], [21, 4, 3, 1], [28, 4, 3, 1], [42, 4, 3, 1], [84, 4, 6, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^4\\times C_6)', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 2], [2, 14, 2], [2, 21, 2], [3, 2, 1], [4, 2, 1], [4, 42, 1], [6, 2, 1], [6, 28, 2], [7, 2, 3], [12, 4, 1], [14, 2, 3], [14, 12, 6], [21, 4, 3], [28, 4, 3], [42, 4, 3], [84, 4, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 150, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 2], [2, 14, 1, 2], [2, 21, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [4, 42, 1, 1], [6, 2, 1, 1], [6, 28, 1, 2], [7, 2, 3, 1], [12, 4, 1, 1], [14, 2, 3, 1], [14, 12, 3, 2], [21, 4, 3, 1], [28, 4, 3, 1], [42, 4, 3, 1], [84, 4, 6, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2688, 'exponent': 84, 'exponents_of_order': [4, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[4, 0, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '168.50', 'hash': 150, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 42], 'inner_gens': [[1, 2, 284], [1, 2, 220], [57, 122, 4]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': True, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 18], [4, 16]], 'label': '336.150', 'linC_count': 6, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 36, 'linQ_dim': 10, 'linQ_dim_count': 36, 'linR_count': 132, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12:D14', 'ngens': 6, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 42, 'number_divisions': 23, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 68, 'number_subgroup_classes': 108, 'number_subgroups': 756, 'old_label': None, 'order': 336, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 83], [3, 2], [4, 44], [6, 58], [7, 6], [12, 4], [14, 78], [21, 12], [28, 12], [42, 12], [84, 24]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 252], 'outer_gens': [[1, 2, 116], [169, 2, 4], [85, 86, 20]], 'outer_group': '24.15', 'outer_hash': 15, 'outer_nilpotent': True, 'outer_order': 24, 'outer_permdeg': 9, 'outer_perms': [24, 40320, 723], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times C_6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 1], [6, 4], [12, 3], [24, 1]], 'representations': {'PC': {'code': 13383365234786736345857771939946251, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -2, -3, -7, 5114, 1988, 50, 5571, 1257, 69, 3844, 3130, 118, 5195]}, 'GLZN': {'d': 2, 'p': 42, 'gens': [2173837, 2148581, 74341, 3063199, 1667863, 963271]}, 'Perm': {'d': 14, 'gens': [997920127, 997960320, 6745939200, 13412044800, 403200, 973]}}, 'schur_multiplier': [2, 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_{12}:D_{14}', 'transitive_degree': 84, 'wreath_data': None, 'wreath_product': False}
