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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '8192.sv', 'ambient_counter': 490, 'ambient_order': 8192, 'ambient_tex': 'C_8^2.C_2^3:D_8', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 32, 'counter': 2841, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '8192.sv.256._.VI', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '256.VI', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '256.5425', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 256, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{16}.D_8', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '32.36', 'subgroup_hash': None, 'subgroup_order': 32, 'subgroup_tex': 'C_2^2\\times C_8', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '8192.sv', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [770567, 442397, 311833], 'label': '8192.sv.256._.VI', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '256.VI', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '256._.VI', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '32.36', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4], [3, 2, 4], [1, 2, 28], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 18, 4], [17, 2, 4], [1, 2, 20]], 'aut_group': '384.20089', 'aut_hash': 20089, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 384, 'aut_permdeg': 10, 'aut_perms': [374407, 1, 823080, 2810574, 2003886, 367920, 5160, 368046], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [4, 1, 2, 1], [4, 1, 6, 1], [8, 1, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '384.20089', 'autcent_hash': 20089, 'autcent_nilpotent': False, 'autcent_order': 384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4:S_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], [2, 1, 7], [4, 1, 8], [8, 1, 16]], 'center_label': '32.36', 'center_order': 32, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 36, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['8.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [4, 1, 2, 4], [8, 1, 4, 4]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 28, 'exponent': 8, 'exponents_of_order': [5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '8.5', 'hash': 36, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 4], [1, 2, 4], [1, 2, 4]], '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, 32]], 'label': '32.36', 'linC_count': 1792, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 48, 'linQ_dim': 6, 'linQ_dim_count': 48, 'linR_count': 96, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*C8', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 32, 'number_divisions': 16, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 38, 'number_subgroups': 38, 'old_label': None, 'order': 32, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 7], [4, 8], [8, 16]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[3, 2, 4], [1, 2, 28], [2, 3, 4], [1, 2, 6], [1, 2, 7], [1, 18, 4], [17, 2, 4], [1, 2, 20]], 'outer_group': '384.20089', 'outer_hash': 20089, 'outer_nilpotent': False, 'outer_order': 384, 'outer_permdeg': 10, 'outer_perms': [374407, 1, 823080, 2810574, 2003886, 367920, 5160, 368046], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^4:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 12, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 4]], 'representations': {'PC': {'code': 557068, 'gens': [1, 2, 3], 'pres': [5, -2, 2, 2, -2, -2, 42, 58]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [25038659807093174, 125101739941717066, 24992906222183252]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [34876415, 3397304, 28816400, 3054512, 28233362]}, 'Perm': {'d': 12, 'gens': [40176, 362880, 39916800, 16582, 5167]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 8], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times C_8', 'transitive_degree': 32, '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': '64.246', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[981723, 441327, 827657, 958613, 754345, 893843], [973387, 764205, 40961, 958613, 630957, 893843], [387549, 39419, 40961, 434821, 172923, 893843], [256577, 624673, 303897, 958613, 230329, 893331], [362589, 887609, 827657, 434821, 508849, 369027], [494041, 780349, 565777, 958613, 385205, 369027], [370765, 1035069, 844041, 189325, 753833, 123019], [956619, 579819, 827657, 959125, 107197, 369539], [440395, 633385, 581649, 713629, 172411, 123019], [502473, 432631, 57857, 188813, 172411, 647323], [587863, 379689, 827657, 434309, 385973, 893331], [432475, 440559, 827657, 434309, 697195, 893843], [887773, 981247, 41473, 434821, 754601, 893843], [502601, 711679, 844041, 713629, 697195, 647835], [756417, 248357, 57345, 713629, 573807, 647835], [1026393, 108841, 319769, 189325, 909989, 123531], [318031, 649273, 57857, 188813, 910245, 123531], [641621, 1026853, 565777, 959125, 508593, 369539]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 16777216, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 4096.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 4, 1], [2, 2, 1, 4], [2, 2, 2, 4], [2, 32, 2, 1], [4, 1, 2, 2], [4, 1, 4, 1], [4, 2, 1, 6], [4, 2, 2, 11], [4, 4, 1, 8], [4, 8, 2, 8], [4, 32, 2, 3], [4, 32, 16, 1], [8, 1, 4, 2], [8, 1, 8, 1], [8, 2, 2, 2], [8, 2, 4, 13], [8, 2, 8, 2], [8, 4, 1, 8], [8, 4, 2, 24], [8, 4, 4, 8], [8, 8, 1, 8], [8, 8, 2, 4], [8, 8, 4, 4], [8, 32, 4, 4], [8, 32, 8, 1], [8, 32, 16, 1], [16, 8, 32, 2], [16, 8, 64, 1], [16, 32, 16, 2], [16, 32, 32, 3]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 12], [2, 32, 2], [4, 1, 8], [4, 2, 28], [4, 4, 8], [4, 8, 16], [4, 32, 22], [8, 1, 16], [8, 2, 72], [8, 4, 88], [8, 8, 32], [8, 32, 40], [16, 8, 128], [16, 32, 128]], 'center_label': '32.36', 'center_order': 32, 'central_product': None, 'central_quotient': '256.3603', 'commutator_count': 2, 'commutator_label': '128.456', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 490, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 12], [2, 32, 1, 2], [4, 1, 2, 4], [4, 2, 1, 12], [4, 2, 2, 8], [4, 4, 1, 8], [4, 8, 1, 16], [4, 32, 1, 6], [4, 32, 2, 8], [8, 1, 4, 4], [8, 2, 2, 8], [8, 2, 4, 14], [8, 4, 1, 4], [8, 4, 2, 26], [8, 4, 4, 8], [8, 8, 1, 8], [8, 8, 2, 12], [8, 32, 2, 12], [8, 32, 4, 4], [16, 8, 8, 16], [16, 32, 4, 24], [16, 32, 8, 4]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': None, 'exponent': 16, 'exponents_of_order': [13], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '512.87977', 'frattini_quotient': '16.14', 'hash': 915567358179400605, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [4, 8, 4, 4, 2, 4], 'inner_gens': [[981723, 895009, 844553, 189325, 172923, 647323], [895069, 441327, 565777, 958613, 172155, 369539], [964827, 195575, 827657, 958613, 508593, 893843], [195539, 441327, 827657, 958613, 508081, 893843], [756673, 772901, 582161, 713629, 754345, 647323], [195539, 965119, 827657, 958613, 1032865, 893843]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 256, 'inner_split': None, 'inner_tex': '(C_2\\times C_8).D_8', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 64], [2, 240], [4, 256], [8, 48]], 'label': '8192.sv', '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': 'C8^2.C2^3:D8', 'ngens': 4, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [1, 7, 35, 107, 267, 555, 739, 579, 291, 139, 75, 43, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 144, 'number_characteristic_subgroups': 2370, 'number_conjugacy_classes': 608, 'number_divisions': 228, 'number_normal_subgroups': 2854, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 8192, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 95], [4, 928], [8, 2048], [16, 5120]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 65536, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 8], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 32], [4, 84], [8, 48], [16, 24], [32, 24]], 'representations': {'PC': {'code': '46534720569278400748565549066835962892883716582230668674910577635059082095766006067386481622882250523446345218472512123537457943522692543', 'gens': [1, 4, 6, 8, 9, 11], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 26, 66, 5020, 39523, 13536, 146, 134164, 27096, 47429, 60884, 226, 47365, 652295, 2178, 91736, 44949, 116111, 50604, 23473, 8042, 2673, 346, 1025034, 27505, 4118, 426, 958475, 3859, 466]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [33025, 557073, 309471, 33281, 294921, 500255, 98307, 573953, 32803, 32785, 109333, 303897, 32905]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 8], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 8, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_8^2.C_2^3:D_8', 'transitive_degree': None, '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': 16, 'aut_gen_orders': [8, 8, 8, 8, 16, 4, 8], 'aut_gens': [[1, 2, 16], [5, 42, 144], [141, 162, 240], [133, 114, 240], [133, 10, 176], [5, 254, 16], [137, 70, 176], [129, 122, 48]], 'aut_group': None, 'aut_hash': 593374907856038680, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 72, 'aut_perms': [57928636994571521390973387799190076155968798548815301727971947107484578613389877585237903938958936697911, 41565968657929463655986870976336697777171849993075727360710377010225163304534702052751454384908618753677, 38980087093771576531551636782238692310143685396098822766726995649533230668394189212982337776103902677957, 53251987600557728535913730770371404344698787061657782796975199036538114664865453826261305883502247673039, 10190515334466711180818049838637739344314102331070185268445186284447004143516330839487979663788357420946, 6280456480583323210825597938322557465060899460581566242918850099392147454349172323049578383881855499999, 32924853948485143239011975444425746518308227167587955364971548786179355314111635468992720832979994574532], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 8, 1, 1], [4, 2, 1, 2], [4, 4, 2, 1], [4, 8, 1, 1], [4, 32, 2, 1], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 2, 1], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 4, 1], [16, 16, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2.C_4^3.C_2^5', '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': 8, 'autcentquo_group': '512.10483248', 'autcentquo_hash': 5580842273875875444, 'autcentquo_nilpotent': True, 'autcentquo_order': 512, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_4^2:C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 8, 1], [4, 2, 2], [4, 4, 2], [4, 8, 1], [4, 32, 2], [8, 2, 4], [8, 4, 2], [8, 8, 2], [16, 2, 4], [16, 4, 6], [16, 8, 4], [16, 16, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '128.399', 'commutator_count': 1, 'commutator_label': '32.3', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5425, '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, 8, 1, 1], [4, 2, 1, 2], [4, 4, 1, 2], [4, 8, 1, 1], [4, 32, 1, 2], [8, 2, 2, 2], [8, 4, 1, 2], [8, 8, 2, 1], [16, 2, 4, 1], [16, 4, 2, 1], [16, 4, 4, 1], [16, 8, 4, 1], [16, 16, 2, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1344, 'exponent': 16, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[4, -1, 8]], 'familial': False, 'frattini_label': '32.3', 'frattini_quotient': '8.5', 'hash': 5425, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 8, 'inner_gen_orders': [2, 8, 8], 'inner_gens': [[1, 14, 16], [133, 2, 240], [1, 34, 16]], 'inner_hash': 399, 'inner_nilpotent': True, 'inner_order': 128, 'inner_split': False, 'inner_tex': 'C_8:D_8', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 18], [4, 11]], 'label': '256.5425', 'linC_count': 8, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 2, 'linQ_dim': 32, 'linQ_dim_count': 2, 'linR_count': 8, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C16.D8', 'ngens': 3, 'nilpotency_class': 4, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 37, 'number_divisions': 22, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 82, 'number_subgroup_classes': 107, 'number_subgroups': 319, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 11], [4, 84], [8, 32], [16, 128]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [16, 0, 64, 0], 'outer_gens': [[1, 18, 16], [129, 2, 240], [1, 10, 16], [1, 2, 80]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [362880, 5040, 120, 9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 64, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 6], [8, 2], [16, 2]], 'representations': {'PC': {'code': 10759575582201494380796581920767411198, 'gens': [1, 2, 5], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 225, 41, 3362, 66, 4355, 539, 4812, 116, 5389, 141, 5390, 166]}, 'Perm': {'d': 64, 'gens': [66450134624445933678799560050331607746391532584685435254529204790382042061733888000000000, 44320550212058861796589790906002973487639595198274528990377915885996743223267447294622038, 16116754647525886103169130832883889877597823742414793216380478825221577993660115377372856, 8058377180213801897373328225453205837655325156463172012191076551884877043098396222780856, 12087040917006856825820464386751442449456779291427783372556125414865848445276683553449656, 4028664439651445760304855308136396429713341927997617409871981318782482722497452481942982, 6010765313484600225807159681127960740186976874672868603891438014304108462838676947041862, 1983116034341975454789449189498620955194254460449807567074683265838922666583379392681647]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{16}.D_8', 'transitive_degree': 64, 'wreath_data': None, 'wreath_product': False}
