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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '256.26960', 'ambient_counter': 26960, 'ambient_order': 256, 'ambient_tex': 'C_2^2\\times \\OD_{64}', 'central': True, 'central_factor': False, 'centralizer_order': 256, 'characteristic': True, 'core_order': 2, 'counter': 55, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '256.26960.128.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '128.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '128.2136', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2136, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 128, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^3\\times C_{16}', 'simple': True, 'solvable': True, 'special_labels': ['D', 'L1', 'D1', 'C7'], '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': '256.26960', 'aut_centralizer_order': 24576, 'aut_label': '128.b1', 'aut_quo_index': 56, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 24576, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['64.a1', '64.c1', '64.d1', '64.e1', '64.f1'], 'contains': ['256.a1'], 'core': '128.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7350, 6961, 7367, 6836], 'generators': [33281], 'label': '256.26960.128.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '128.b1', 'normal_contained_in': ['64.a1', '64.c1', '64.d1', '64.e1', '64.f1'], 'normal_contains': ['256.a1'], 'normalizer': '1.a1', 'old_label': '128.b1', 'projective_image': '128.2136', 'quotient_action_image': '1.1', 'quotient_action_kernel': '128.2136', 'quotient_action_kernel_order': 128, 'quotient_fusion': None, 'short_label': '128.b1', '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': '128.2136', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 24, 8, 24], 'aut_gens': [[557073, 491535, 32785, 32801], [557585, 492047, 557569, 492351], [557073, 492047, 33297, 33329], [491535, 1016351, 1016335, 1016191], [557073, 1016351, 557569, 492223], [491535, 1016351, 491551, 33121]], 'aut_group': None, 'aut_hash': 1782545609031500528, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24576, 'aut_permdeg': 66, 'aut_perms': [117850745636966563518350935616491415685336112059370827455326223686677003634596819974010281694, 167563402277213889188069835553151426146413376679092434111579003094967769582787220336083240969, 33930361776115380563774728997164775585674145133401419071358651997510916819532156017755534521, 150115334226458361598914606623508939203115572838951960317231278526081756473755614224951871406, 451403274117678737355201847936420346669526286353199487316569074806988728345744692035513734726], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 6, 1], [2, 2, 4, 1], [4, 1, 2, 1], [4, 1, 6, 1], [4, 2, 4, 1], [8, 1, 4, 1], [8, 1, 12, 1], [8, 2, 8, 1], [16, 1, 8, 1], [16, 1, 24, 1], [16, 2, 16, 1], [32, 2, 64, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^4.C_2^4.D_6.C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': None, 'autcent_hash': 6195787851592176878, 'autcent_nilpotent': False, 'autcent_order': 12288, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^4.C_2^4.D_6.C_2^2', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 2, 4], [4, 1, 8], [4, 2, 4], [8, 1, 16], [8, 2, 8], [16, 1, 32], [16, 2, 16], [32, 2, 64]], 'center_label': '64.183', 'center_order': 64, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', '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': 26960, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['64.51', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 2, 1, 4], [4, 1, 2, 4], [4, 2, 1, 4], [8, 1, 4, 4], [8, 2, 2, 4], [16, 1, 8, 4], [16, 2, 4, 4], [32, 2, 8, 8]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 53760, 'exponent': 32, 'exponents_of_order': [8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.1', 'frattini_quotient': '16.14', 'hash': 26960, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [1, 1, 2, 2], 'inner_gens': [[557073, 491535, 32785, 32801], [557073, 491535, 32785, 32801], [557073, 491535, 32785, 33313], [557073, 491535, 33297, 32801]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 128], [2, 32]], 'label': '256.26960', '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': 'C2^2*OD64', 'ngens': 4, 'nilpotency_class': 2, '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': 14, 'number_characteristic_subgroups': 17, 'number_conjugacy_classes': 160, 'number_divisions': 44, 'number_normal_subgroups': 231, 'number_subgroup_autclasses': 57, 'number_subgroup_classes': 251, 'number_subgroups': 271, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 15], [4, 16], [8, 32], [16, 64], [32, 128]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [4, 4, 4, 3, 12], 'outer_gen_pows': [32785, 32769, 32785, 33697, 32785], 'outer_gens': [[557585, 1015839, 33297, 1016191], [557585, 1016351, 491551, 557729], [1016351, 492047, 1016335, 492463], [492047, 1015839, 491551, 557617], [492047, 1016351, 492063, 33185]], 'outer_group': None, 'outer_hash': 461510131664947659, 'outer_nilpotent': False, 'outer_order': 6144, 'outer_permdeg': 18, 'outer_perms': [85272824287462, 1471407653329217, 89115893396062, 1588369845720, 2262277615182622], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^6.C_6.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 36, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 16], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 8], [8, 8], [16, 4]], 'representations': {'PC': {'code': 148154952400858251384, 'gens': [1, 2, 3, 4], 'pres': [8, -2, 2, 2, 2, -2, -2, -2, -2, 1107, 91, 116, 141, 166]}, 'GLZN': {'d': 2, 'p': 51, 'gens': [4613749, 132667, 3316300, 2122432, 3273816, 663260, 6101992, 1724476]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [32801, 33281, 557073, 32833, 491535, 32785, 32897, 33025]}, 'Perm': {'d': 36, 'gens': [10959433346687773912788413004267245310127, 1485118934590953300150943468630531815967, 22144361263315068909386751450970303815856, 23, 32841173109747357328416314341367398653360, 43480038270632073028996115235757504494240, 54117420931580933449279810330023105073440, 22144361263315068909386751450970303815840]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 16], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times \\OD_{64}', 'transitive_degree': 128, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '128.2136', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 168, 'aut_gen_orders': [2, 2, 2, 2, 4, 4, 2, 2, 2, 2], 'aut_gens': [[1, 2, 4, 8], [70, 2, 67, 79], [1, 2, 4, 15], [1, 2, 4, 72], [1, 67, 69, 8], [1, 2, 4, 24], [1, 2, 4, 104], [65, 2, 68, 72], [1, 2, 4, 77], [1, 71, 4, 77], [1, 2, 4, 73]], 'aut_group': '86016.bk', 'aut_hash': 3270269662069206077, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 86016, 'aut_permdeg': 34, 'aut_perms': [144837903429120095961757595345979273720, 1920833431893351976830076735493046, 18684210223057525662467576180300790966, 118064606089713125444838326400371758080, 8980437409661352453257127716943575047, 52103747306013426605553945216122908080, 144840469689942105726824542131498651774, 18682617177822394450571338564155941046, 100023423486098033691920128413066110934, 18684209003500424626973511562010926080], 'aut_phi_ratio': 1344.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 14, 1], [4, 1, 2, 1], [4, 1, 14, 1], [8, 1, 4, 1], [8, 1, 28, 1], [16, 1, 64, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4.C_2^7:\\GL(3,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 168, 'autcent_group': '86016.bk', 'autcent_hash': 3270269662069206077, 'autcent_nilpotent': False, 'autcent_order': 86016, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_4.C_2^7:\\GL(3,2)', '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, 15], [4, 1, 16], [8, 1, 32], [16, 1, 64]], 'center_label': '128.2136', 'center_order': 128, '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', '2.1', '2.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 2136, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16.1', 1], ['2.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 15], [4, 1, 2, 8], [8, 1, 4, 8], [16, 1, 8, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 960, 'exponent': 16, 'exponents_of_order': [7], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.1', 'frattini_quotient': '16.14', 'hash': 2136, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8], [1, 2, 4, 8]], '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, 128]], 'label': '128.2136', 'linC_count': None, 'linC_degree': 4, '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': 'C2^3*C16', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 128, 'number_divisions': 40, 'number_normal_subgroups': 220, 'number_subgroup_autclasses': 26, 'number_subgroup_classes': 220, 'number_subgroups': 220, 'old_label': None, 'order': 128, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 15], [4, 16], [8, 32], [16, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 168, 'outer_gen_orders': [2, 2, 2, 2, 4, 4, 2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[70, 2, 67, 79], [1, 2, 4, 15], [1, 2, 4, 72], [1, 67, 69, 8], [1, 2, 4, 24], [1, 2, 4, 104], [65, 2, 68, 72], [1, 2, 4, 77], [1, 71, 4, 77], [1, 2, 4, 73]], 'outer_group': '86016.bk', 'outer_hash': 3270269662069206077, 'outer_nilpotent': False, 'outer_order': 86016, 'outer_permdeg': 34, 'outer_perms': [144837903429120095961757595345979273720, 1920833431893351976830076735493046, 18684210223057525662467576180300790966, 118064606089713125444838326400371758080, 8980437409661352453257127716943575047, 52103747306013426605553945216122908080, 144840469689942105726824542131498651774, 18682617177822394450571338564155941046, 100023423486098033691920128413066110934, 18684209003500424626973511562010926080], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_4.C_2^7:\\GL(3,2)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 16], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 8], [8, 8]], 'representations': {'PC': {'code': 2233919864888, 'gens': [1, 2, 3, 4], 'pres': [7, -2, 2, 2, 2, -2, -2, -2, 80, 102, 124]}, 'GLZN': {'d': 2, 'p': 28, 'gens': [28573, 562037, 285389, 22345, 30431, 111609, 337745]}, 'GLZq': {'d': 2, 'q': 32, 'gens': [102991, 565385, 33041, 1032719, 33281, 557073, 573969]}, 'Perm': {'d': 22, 'gens': [20916435456000, 121645100408832000, 355687428096000, 51090942171709440000, 9703614452976, 4097506710982, 1313941673647]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 16], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^3\\times C_{16}', 'transitive_degree': 128, 'wreath_data': None, 'wreath_product': False}
