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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.845', 'ambient_counter': 845, 'ambient_order': 960, 'ambient_tex': 'C_4:C_{20}.C_{12}', 'central': False, 'central_factor': False, 'centralizer_order': 240, 'characteristic': True, 'core_order': 5, 'counter': 115, 'cyclic': True, 'direct': False, 'hall': 5, 'label': '960.845.192.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '192.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '192.138', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 138, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 192, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}.D_8', 'simple': True, 'solvable': True, 'special_labels': ['L3', 'C7'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '5.1', 'subgroup_hash': 1, 'subgroup_order': 5, 'subgroup_tex': 'C_5', 'supersolvable': True, 'sylow': 5}
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gps_subgroup_data • Show schema
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{'ambient': '960.845', 'aut_centralizer_order': 640, 'aut_label': '192.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '4.1', 'aut_weyl_index': 640, 'centralizer': '4.a1.a1', 'complements': ['5.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['64.a1.a1', '96.a1.a1', '96.b1.a1', '96.c1.a1'], 'contains': ['960.a1.a1'], 'core': '192.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7769, 2017, 7785, 8315, 6092, 4775, 3535, 4775], 'generators': [192], 'label': '960.845.192.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '192.a1.a1', 'normal_contained_in': ['64.a1.a1', '96.b1.a1', '96.a1.a1', '96.c1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '192.a1.a1', 'projective_image': '960.845', 'quotient_action_image': '4.1', 'quotient_action_kernel': '48.22', 'quotient_action_kernel_order': 48, 'quotient_fusion': None, 'short_label': '192.a1.a1', 'subgroup_fusion': None, 'weyl_group': '4.1'}
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gps_groups • Show schema
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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}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 20, 'aut_gen_orders': [4, 4, 10, 10, 4, 4, 2], 'aut_gens': [[1, 4, 16], [481, 732, 760], [729, 12, 688], [337, 12, 176], [49, 484, 176], [481, 732, 696], [633, 4, 368], [337, 492, 944]], 'aut_group': None, 'aut_hash': 8812755448905254656, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2560, 'aut_permdeg': 50, 'aut_perms': [1258930672194521426732282217026195847624257575647612871742337164, 8702237407301105088507636379370297825426509629128529068766453699, 9911440841365432176158972619502026193075522110722350562108217835, 1256002038950170874275163493402738586066926455382804438746760773, 8702496031937085686343035804600319857268526674696937013947786840, 11784312567274484261217524414843156706183917205133018836534806841, 11787009978863157079061700083895318242282195837079795309076951667], 'aut_phi_ratio': 10.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 4, 1, 1], [4, 8, 1, 1], [4, 10, 1, 4], [4, 40, 1, 1], [5, 4, 1, 1], [6, 1, 2, 3], [8, 20, 2, 4], [10, 4, 1, 3], [12, 4, 2, 1], [12, 8, 2, 1], [12, 10, 2, 4], [12, 40, 2, 1], [15, 4, 2, 1], [20, 8, 2, 1], [20, 8, 4, 1], [24, 20, 4, 4], [30, 4, 2, 3], [60, 8, 4, 1], [60, 8, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_5:(C_2^4.C_2^5)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 20, 'autcentquo_group': '80.50', 'autcentquo_hash': 50, 'autcentquo_nilpotent': False, 'autcentquo_order': 80, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 4, 1], [4, 8, 1], [4, 10, 4], [4, 40, 1], [5, 4, 1], [6, 1, 6], [8, 20, 8], [10, 4, 3], [12, 4, 2], [12, 8, 2], [12, 10, 8], [12, 40, 2], [15, 4, 2], [20, 8, 6], [24, 20, 16], [30, 4, 6], [60, 8, 12]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '80.34', 'commutator_count': 1, 'commutator_label': '40.9', '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': 845, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['320.211', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 4, 1, 1], [4, 8, 1, 1], [4, 10, 1, 4], [4, 40, 1, 1], [5, 4, 1, 1], [6, 1, 2, 3], [8, 20, 4, 2], [10, 4, 1, 3], [12, 4, 2, 1], [12, 8, 2, 1], [12, 10, 2, 4], [12, 40, 2, 1], [15, 4, 2, 1], [20, 8, 2, 1], [20, 8, 4, 1], [24, 20, 8, 2], [30, 4, 2, 3], [60, 8, 4, 1], [60, 8, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 96, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.40', 'hash': 845, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [4, 2, 10], 'inner_gens': [[1, 252, 696], [729, 4, 496], [297, 484, 16]], 'inner_hash': 34, 'inner_nilpotent': False, 'inner_order': 80, 'inner_split': True, 'inner_tex': 'D_{10}:C_4', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 30], [4, 27], [8, 6]], 'label': '960.845', 'linC_count': 256, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 88, 'linQ_dim': 14, 'linQ_dim_count': 16, 'linR_count': 40, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4:C20.C12', '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': 42, 'number_characteristic_subgroups': 52, 'number_conjugacy_classes': 87, 'number_divisions': 38, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': 128, 'number_subgroup_classes': 128, 'number_subgroups': 564, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 92], [5, 4], [6, 6], [8, 160], [10, 12], [12, 184], [15, 8], [20, 48], [24, 320], [30, 24], [60, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 4, 656], [9, 4, 16], [481, 4, 16], [1, 244, 504]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [120, 5040, 362880, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 11], [8, 10], [16, 4], [32, 1]], 'representations': {'PC': {'code': 25784213879252786177242584625319914651947573621140168714841686023, 'gens': [1, 3, 5], 'pres': [8, -2, -2, -2, -2, 2, -2, -3, -5, 16, 73, 6050, 154, 66, 27844, 15692, 4980, 116, 19973, 14605, 141, 46598, 7182, 222, 36871, 24591]}, 'GLZN': {'d': 2, 'p': 105, 'gens': [2039957, 34456834, 82191446, 18522016, 35942036, 87979576, 1159831, 53589154]}, 'Perm': {'d': 24, 'gens': [27134521033991338155744, 3432837896607665508480, 3, 56210133292293718444560, 83436502779364440787200, 6719953726080, 56210133294621698878080, 6000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4:C_{20}.C_{12}', 'transitive_degree': 960, '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': '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, 4, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 16], [1, 6, 16], [5, 2, 16], [1, 106, 16], [97, 2, 16], [1, 150, 112], [61, 2, 112], [1, 2, 80]], 'aut_group': '512.10493114', 'aut_hash': 2216133851576011484, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 512, 'aut_permdeg': 34, 'aut_perms': [3695786416542731629507777773672541044, 125369237118155089932589986031681123859, 7119405074906467719416291380508447822, 232647201180195425643561696305549758080, 5292865063864490595708948730328383524, 162587396504279235595970498932845177720, 2450415076490809314868101120000], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [6, 1, 2, 3], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 4, 1], [24, 4, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^3\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': True, 'autcentquo_cyclic': False, 'autcentquo_exponent': 2, 'autcentquo_group': '16.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': True, 'autcentquo_order': 16, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 1, 2], [4, 2, 4], [4, 4, 1], [4, 8, 2], [6, 1, 6], [8, 4, 8], [12, 2, 8], [12, 4, 2], [12, 8, 4], [24, 4, 16]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '16.3', 'commutator_count': 1, 'commutator_label': '8.2', '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': 138, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['64.13', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [6, 1, 2, 3], [8, 4, 4, 2], [12, 2, 2, 4], [12, 4, 2, 1], [12, 8, 2, 2], [24, 4, 8, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.2', 'frattini_quotient': '12.5', 'hash': 138, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 2], 'inner_gens': [[1, 150, 112], [61, 2, 112], [97, 98, 16]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': True, 'inner_tex': 'C_2^2:C_4', 'inner_used': [1, 2], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 30], [4, 3]], 'label': '192.138', 'linC_count': 128, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 10, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12.D8', 'ngens': 7, 'nilpotency_class': 3, 'nilpotent': True, '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': 24, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 57, 'number_divisions': 26, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 58, 'number_subgroup_classes': 64, 'number_subgroups': 114, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [6, 6], [8, 32], [12, 56], [24, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2], 'outer_gen_pows': [0, 4, 0, 0, 0], 'outer_gens': [[1, 6, 16], [5, 2, 16], [1, 106, 16], [97, 2, 16], [1, 2, 80]], 'outer_group': '32.51', 'outer_hash': 51, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 32, 'outer_perms': [8259470424175296574426514081379841, 17774154876782283574170730336362004, 26330869002213901050922466899460658, 34830753587784208264754691194221536, 43328107513216344878530623767946840], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [4, 9], [8, 5]], 'representations': {'PC': {'code': 127579648312838695058256526209, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 56, 2101, 36, 254, 58, 3924, 1971, 102, 124]}, 'GLZN': {'d': 2, 'p': 21, 'gens': [102661, 120406, 80557, 74096, 19311, 37048, 38503]}, 'Perm': {'d': 19, 'gens': [1153381250700960, 7222372716562680, 4, 13917765117696744, 8448744, 20713823523993600, 20713823536535304]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.D_8', 'transitive_degree': 192, 'wreath_data': None, 'wreath_product': False}
