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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '256.23466', 'ambient_counter': 23466, 'ambient_order': 256, 'ambient_tex': 'C_4.D_4^2', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 64, 'counter': 42, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '256.23466.4.z1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '4.z1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '64.92', 'subgroup_hash': 92, 'subgroup_order': 64, 'subgroup_tex': '\\OD_{16}:C_2^2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '256.23466', 'aut_centralizer_order': 16, 'aut_label': '4.z1', 'aut_quo_index': 6, 'aut_stab_index': 1, 'aut_weyl_group': '256.55683', 'aut_weyl_index': 16, 'centralizer': '64.a1.a1', 'complements': ['64.bk1.a1', '64.bk1.a2', '64.bk1.b2', '64.bk1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['2.f1.a1', '2.h1.a1', '2.n1.a1'], 'contains': ['8.e1.a1', '8.l1.a1', '8.o1.a1', '8.ec1.a1', '8.ec1.b1'], 'core': '4.z1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5393, 4712, 5786, 6040, 5386, 4728, 5784, 6011], 'generators': [49, 18, 64], 'label': '256.23466.4.z1.a1', 'mobius_quo': 0, 'mobius_sub': 2, 'normal_closure': '4.z1.a1', 'normal_contained_in': ['2.h1.a1', '2.n1.a1', '2.f1.a1'], 'normal_contains': ['8.e1.a1', '8.l1.a1', '8.o1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.z1.a1', 'projective_image': '64.226', 'quotient_action_image': '4.2', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.z1.a1', 'subgroup_fusion': None, 'weyl_group': '64.226'}
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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': 3, 'aut_exponent': 8, 'aut_gen_orders': [2, 2, 2, 2, 4, 4], 'aut_gens': [[63503, 4135, 28807, 30125], [63503, 4135, 28807, 62765], [63503, 28897, 28807, 5091], [63503, 13413, 63631, 4971], [63503, 28897, 63631, 21359], [63503, 28897, 28807, 5059], [28679, 63721, 28807, 4939]], 'aut_group': '1024.ddn', 'aut_hash': 7003003021026862916, 'aut_nilpotency_class': 4, 'aut_nilpotent': True, 'aut_order': 1024, 'aut_permdeg': 16, 'aut_perms': [14153644491235, 6250028757264, 11869428221385, 965715037632, 18347084748815, 9144874513110], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 1, 2], [2, 4, 4, 1], [4, 2, 2, 2], [8, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_2\\times D_4^2):D_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 4, 'autcentquo_group': '32.27', 'autcentquo_hash': 27, 'autcentquo_nilpotent': True, 'autcentquo_order': 32, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2^2\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [2, 4, 4], [4, 2, 4], [8, 4, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '16.3', 'commutator_count': 1, 'commutator_label': '4.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 92, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['32.7', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 4, 1, 4], [4, 2, 1, 4], [8, 4, 2, 4]], 'element_repr_type': 'GLZq', 'elementary': 2, 'eulerian_function': 84, 'exponent': 8, 'exponents_of_order': [6], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '8.5', 'hash': 92, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [1, 2, 2, 4], 'inner_gens': [[63503, 4135, 28807, 30125], [63503, 4135, 28807, 5091], [63503, 4135, 28807, 62885], [63503, 63593, 63631, 30125]], 'inner_hash': 3, 'inner_nilpotent': True, 'inner_order': 16, 'inner_split': False, 'inner_tex': 'C_2^2:C_4', 'inner_used': [2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 4], [4, 2]], 'label': '64.92', 'linC_count': 16, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 8, 'linQ_dim': 5, 'linQ_dim_count': 8, 'linR_count': 8, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'OD16:C2^2', 'ngens': 3, 'nilpotency_class': 3, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 9, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 22, 'number_divisions': 18, 'number_normal_subgroups': 41, 'number_subgroup_autclasses': 41, 'number_subgroup_classes': 93, 'number_subgroups': 185, 'old_label': None, 'order': 64, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 23], [4, 8], [8, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [13451, 4097, 4097, 4097, 4097], 'outer_gens': [[28679, 54315, 63631, 54119], [63503, 63721, 28807, 30125], [28679, 4135, 28807, 30125], [63503, 4135, 63631, 13737], [28679, 28897, 28807, 5059]], 'outer_group': '64.202', 'outer_hash': 202, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [367925, 362885, 368056, 16, 1169289], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3:D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 2]], 'representations': {'PC': {'code': 17905787885592, 'gens': [1, 2, 3, 4], 'pres': [6, 2, 2, 2, 2, 2, 2, 153, 255, 69, 730, 88]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706304316034, 706461441036]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [6210625, 32667734, 19208257, 18750531, 6670401, 6276161]}, 'GLZq': {'d': 2, 'q': 16, 'gens': [4225, 63503, 39049, 37731, 5059, 54277]}, 'Perm': {'d': 10, 'gens': [420031, 142584, 1, 126774, 899688, 1229808]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\OD_{16}:C_2^2', 'transitive_degree': 16, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 2, 2, 2, 4, 2, 4], 'aut_gens': [[1, 2, 8, 16, 32], [1, 2, 8, 16, 40], [1, 2, 8, 24, 32], [1, 10, 8, 16, 32], [9, 2, 8, 16, 32], [1, 2, 8, 16, 160], [1, 130, 8, 16, 32], [1, 134, 8, 16, 104], [133, 2, 8, 216, 40], [1, 74, 8, 16, 224], [201, 10, 8, 80, 32]], 'aut_group': None, 'aut_hash': 2978329760197401528, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 4096, 'aut_permdeg': 32, 'aut_perms': [203824972580776372143719351208990, 119041069717234183495534129042375021, 217819123471898259228985230, 3722698198699129546235592925394916, 26862887493669208962017078501094, 47179935535914199253854134, 238083298749040741870414495385195810, 137706525201601278321257568881684211, 237994667311976659211801996078904050, 260009706724647004684754357020560938], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [2, 8, 1, 3], [2, 8, 2, 1], [2, 16, 1, 1], [4, 2, 1, 4], [4, 8, 1, 5], [4, 8, 2, 1], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 2], [8, 8, 2, 2], [8, 16, 1, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times D_4^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '256.56092', 'autcent_hash': 56092, 'autcent_nilpotent': True, 'autcent_order': 256, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^8', '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], [2, 2, 2], [2, 8, 5], [2, 16, 1], [4, 2, 4], [4, 8, 7], [4, 16, 2], [8, 4, 4], [8, 8, 6], [8, 16, 2]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '64.226', 'commutator_count': 1, 'commutator_label': '16.10', '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': 23466, '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], [2, 8, 1, 5], [2, 16, 1, 1], [4, 2, 1, 4], [4, 8, 1, 5], [4, 8, 2, 1], [4, 16, 1, 2], [8, 4, 2, 2], [8, 8, 1, 6], [8, 16, 1, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 322560, 'exponent': 8, 'exponents_of_order': [8], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '16.10', 'frattini_quotient': '16.14', 'hash': 23466, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 4, 'inner_gen_orders': [2, 4, 1, 2, 4], 'inner_gens': [[1, 134, 8, 16, 104], [133, 2, 8, 216, 40], [1, 2, 8, 16, 32], [1, 74, 8, 16, 224], [201, 10, 8, 80, 32]], 'inner_hash': 226, 'inner_nilpotent': True, 'inner_order': 64, 'inner_split': None, 'inner_tex': 'D_4^2', 'inner_used': [1, 2, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 12], [4, 8], [8, 1]], 'label': '256.23466', 'linC_count': 16, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 12, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C4.D4^2', 'ngens': 4, 'nilpotency_class': 3, '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': 31, 'number_characteristic_subgroups': 105, 'number_conjugacy_classes': 37, 'number_divisions': 34, 'number_normal_subgroups': 115, 'number_subgroup_autclasses': 435, 'number_subgroup_classes': 517, 'number_subgroups': 1575, 'old_label': None, 'order': 256, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 63], [4, 96], [8, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 1, 1, 1, 1], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 8, 16, 40], [1, 2, 8, 24, 32], [1, 10, 8, 16, 32], [9, 2, 8, 16, 32], [1, 2, 8, 16, 160], [1, 130, 8, 16, 32], [1, 2, 8, 16, 32], [1, 2, 8, 16, 32], [1, 2, 8, 16, 32], [1, 2, 8, 16, 32]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 64, 'outer_perms': [1985188526780423877464651544814742829008285424088317476814575392989893856928648616569201, 4154112628923264636632128775345560581811008712804739481245760941829028879006354295684644, 6173192254075958537951841054780675191527474692087413872184429888595485152884157782042258, 8187884636372818974008644669228639103949846608128961376293109726798270309905592527523936, 10202480873618811639456691470785796184518652310898872541961146794314818216777211400698200, 12217075239169549674926007643948061880093513498779373956533360210631363056280464921156320, 0, 0, 0, 0], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 12], [4, 4], [8, 1], [16, 1]], 'representations': {'PC': {'code': 42025826321944811235196774817929442, 'gens': [1, 2, 4, 5, 6], 'pres': [8, 2, 2, 2, 2, 2, 2, 2, 2, 2145, 41, 4332, 1460, 4997, 973, 709, 141, 10758, 710, 166]}, 'Perm': {'d': 20, 'gens': [142051804008439807, 275476516035804841, 153746330118893296, 405851872010785200, 534437383048586760, 656097216588617880, 743265286921923127, 743265286921923120]}}, 'schur_multiplier': [2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_4.D_4^2', 'transitive_degree': 64, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
