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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1440.5010', 'ambient_counter': 5010, 'ambient_order': 1440, 'ambient_tex': 'C_{30}.(C_4\\times D_6)', 'central': False, 'central_factor': False, 'centralizer_order': 6, 'characteristic': True, 'core_order': 360, 'counter': 19, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1440.5010.4.g1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.g1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '360.100', 'subgroup_hash': 100, 'subgroup_order': 360, 'subgroup_tex': 'C_{60}.C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1440.5010', 'aut_centralizer_order': 6, 'aut_label': '4.g1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1920.204530', 'aut_weyl_index': 6, 'centralizer': '240.b1.a1', 'complements': ['360.g1.b1', '360.g1.a1', '360.f1.a1', '360.f1.b1', '360.h1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1.a1'], 'contains': ['8.b1.a1', '8.e1.a1', '8.e1.b1', '12.f1.a1', '12.r1.a1', '20.g1.a1'], 'core': '4.g1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [9501, 7461, 2303, 3049, 8459, 7284, 2708, 6690], 'generators': [5, 288, 960, 720, 360, 8], 'label': '1440.5010.4.g1.a1', 'mobius_quo': 0, 'mobius_sub': 0, 'normal_closure': '4.g1.a1', 'normal_contained_in': ['2.a1.a1'], 'normal_contains': ['8.b1.a1', '8.e1.b1', '8.e1.a1', '12.f1.a1'], 'normalizer': '1.a1.a1', 'old_label': '4.g1.a1', 'projective_image': '720.804', 'quotient_action_image': '4.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '4.g1.a1', 'subgroup_fusion': None, 'weyl_group': '240.195'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '12.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [4, 2, 4, 2, 2, 2, 2, 3, 5], 'aut_gens': [[1, 6], [1, 258], [271, 186], [1, 222], [185, 6], [181, 246], [181, 6], [1, 294], [241, 6], [73, 6]], 'aut_group': '1920.204530', 'aut_hash': 5431080212833723047, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1920, 'aut_permdeg': 62, 'aut_perms': [5119542581924776086608103328688406927443547256925654967735169970985812006751173420, 401582286353246267107058131506746108869617803528300822826010024330166210899648595001, 368148017559451324647394215529157080810989879975268614957653773504823119161375844, 19000484851247594721483460535550044871683032387109039940765462273000569166380992197410, 211566672149062922679592321660701748285416892722965127372809799408034095241645070400, 211554916273959456262777059257306402336582491584640256361276809100242708881016517410, 5144449225348439601981433736051881946027306103891113598815585645384919228685266607, 350273845853490878806761786617525933759012733536464175878209011201082206842173858576, 313094795380282400831068242146446405753454140670511304887954253681569188035952640000], 'aut_phi_ratio': 20.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [4, 30, 2, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 30, 4, 1], [15, 2, 4, 2], [15, 2, 8, 1], [20, 2, 4, 1], [30, 2, 4, 2], [30, 2, 8, 1], [60, 2, 8, 2], [60, 2, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4\\times D_6\\times F_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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '240.195', 'autcentquo_hash': 195, 'autcentquo_nilpotent': False, 'autcentquo_order': 240, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 2, 3], [4, 2, 1], [4, 30, 2], [5, 2, 2], [6, 1, 2], [6, 2, 3], [10, 2, 2], [12, 2, 8], [12, 30, 4], [15, 2, 16], [20, 2, 4], [30, 2, 16], [60, 2, 32]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '60.12', 'commutator_count': 1, 'commutator_label': '30.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 100, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['120.26', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [4, 30, 1, 2], [5, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [10, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [12, 30, 2, 2], [15, 2, 4, 2], [15, 2, 8, 1], [20, 2, 4, 1], [30, 2, 4, 2], [30, 2, 8, 1], [60, 2, 8, 2], [60, 2, 16, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 60, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[2, 0, 16]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '180.34', 'hash': 100, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 30], 'inner_gens': [[1, 354], [13, 6]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'D_{30}', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 4, 'irrep_stats': [[1, 12], [2, 87]], 'label': '360.100', 'linC_count': 16, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 10, 'linQ_dim_count': 4, 'linR_count': 8, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C60.C6', '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, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 99, 'number_divisions': 28, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 46, 'number_subgroup_classes': 54, 'number_subgroups': 180, 'old_label': None, 'order': 360, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 62], [5, 4], [6, 8], [10, 4], [12, 136], [15, 32], [20, 8], [30, 32], [60, 64]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 4], 'outer_gen_pows': [0, 0, 90, 0], 'outer_gens': [[1, 246], [5, 6], [91, 6], [1, 78]], 'outer_group': '32.45', 'outer_hash': 45, 'outer_nilpotent': True, 'outer_order': 32, 'outer_permdeg': 10, 'outer_perms': [127, 362880, 5040, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_4', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 7], [4, 6], [8, 6], [16, 4], [32, 1]], 'representations': {'PC': {'code': 3665395516389975291540363145479, 'gens': [1, 3], 'pres': [6, -2, -3, -2, -2, -3, -5, 12, 1087, 6374, 50, 8355, 69, 10084, 118, 10373]}, 'GLFp': {'d': 2, 'p': 61, 'gens': [10668108, 7036413, 6649]}, 'Perm': {'d': 19, 'gens': [356995585997304, 8448744, 3, 12541704, 6706022400, 7115056236288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 6], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{60}.C_6', 'transitive_degree': 120, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [6, 20, 60, 60, 12, 30, 2], 'aut_gens': [[1, 2, 24], [737, 770, 1416], [1081, 218, 24], [1089, 986, 984], [1089, 1130, 984], [361, 34, 168], [1097, 1130, 744], [1, 442, 696]], 'aut_group': None, 'aut_hash': 3555297260956627131, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11520, 'aut_permdeg': 72, 'aut_perms': [17934984785178264638378021674029392721292336189041559975144454882645738827723301681501127934961776587347, 49619403316558637895447253219175843564119549460439016115525801443547264333067592681295854018058317006358, 55513156026908319172435874163365180205628754534825569768007839164365081785545410669990897104247631449412, 55441284375207262871139882109632679118006847574943848515672247766228295892768661871888937606494012813612, 21678845095738879225948798728750813175025317004090499478341374500389015736085087728116709107483606969312, 3084158880278779900543543377706409636344369733744445813072779278364824452506477289449094807185582582211, 191982484347994560268850956851654597459912062108535923872402462698752415162616115120930922437145403242], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 2, 1], [4, 10, 1, 1], [4, 30, 2, 3], [4, 45, 2, 2], [4, 90, 1, 2], [5, 4, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 10, 1, 4], [6, 20, 1, 2], [10, 4, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 12, 2, 1], [12, 20, 1, 2], [12, 20, 2, 1], [12, 60, 2, 3], [15, 4, 2, 1], [15, 8, 1, 1], [15, 8, 2, 1], [20, 8, 1, 1], [20, 24, 2, 1], [30, 4, 2, 1], [30, 8, 1, 1], [30, 8, 2, 1], [60, 8, 2, 2], [60, 8, 4, 1], [60, 24, 4, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times S_3\\times D_5).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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '1440.5889', 'autcentquo_hash': 5889, 'autcentquo_nilpotent': False, 'autcentquo_order': 1440, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_5.D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 5, 2], [3, 2, 2], [3, 4, 1], [4, 2, 1], [4, 6, 2], [4, 10, 1], [4, 30, 6], [4, 45, 4], [4, 90, 2], [5, 4, 1], [6, 2, 2], [6, 4, 1], [6, 10, 4], [6, 20, 2], [10, 4, 1], [12, 4, 4], [12, 12, 2], [12, 20, 4], [12, 60, 6], [15, 4, 2], [15, 8, 3], [20, 8, 1], [20, 24, 2], [30, 4, 2], [30, 8, 3], [60, 8, 8], [60, 24, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '720.804', 'commutator_count': 1, 'commutator_label': '90.10', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 5010, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 5, 1, 2], [3, 2, 1, 2], [3, 4, 1, 1], [4, 2, 1, 1], [4, 6, 1, 2], [4, 10, 1, 1], [4, 30, 1, 2], [4, 30, 2, 2], [4, 45, 2, 2], [4, 90, 2, 1], [5, 4, 1, 1], [6, 2, 1, 2], [6, 4, 1, 1], [6, 10, 1, 4], [6, 20, 1, 2], [10, 4, 1, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 12, 1, 2], [12, 20, 1, 2], [12, 20, 2, 1], [12, 60, 1, 2], [12, 60, 2, 2], [15, 4, 2, 1], [15, 8, 1, 1], [15, 8, 2, 1], [20, 8, 1, 1], [20, 24, 1, 2], [30, 4, 2, 1], [30, 8, 1, 1], [30, 8, 2, 1], [60, 8, 2, 2], [60, 8, 4, 1], [60, 24, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 64512, 'exponent': 60, 'exponents_of_order': [5, 2, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[8, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '720.804', 'hash': 5010, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 12, 30], 'inner_gens': [[1, 10, 744], [17, 2, 1128], [721, 338, 24]], 'inner_hash': 804, 'inner_nilpotent': False, 'inner_order': 720, 'inner_split': True, 'inner_tex': 'D_{10}.S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 16, 'irrep_stats': [[1, 16], [2, 20], [4, 24], [8, 15]], 'label': '1440.5010', 'linC_count': 324, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 384, 'linQ_dim': 12, 'linQ_dim_count': 224, 'linR_count': 16, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C30.(C4*D6)', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 50, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 75, 'number_divisions': 55, 'number_normal_subgroups': 88, 'number_subgroup_autclasses': 234, 'number_subgroup_classes': 310, 'number_subgroups': 2388, 'old_label': None, 'order': 1440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 11], [3, 8], [4, 564], [5, 4], [6, 88], [10, 4], [12, 480], [15, 32], [20, 56], [30, 32], [60, 160]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 360], 'outer_gens': [[1, 10, 24], [1, 2, 984], [721, 10, 24], [361, 362, 24]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 8, 'outer_perms': [5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 19, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 18], [4, 15], [8, 9], [16, 4], [32, 1]], 'representations': {'PC': {'code': 3325937840427595664100828815536067748258052365523813900062952001044743, 'gens': [1, 2, 5], 'pres': [8, -2, -2, -2, -3, -2, -2, -3, -5, 5760, 161, 41, 482, 66, 515, 29764, 22572, 11780, 116, 19597, 10965, 141, 5390, 5398, 222, 18447, 18455]}, 'Perm': {'d': 19, 'gens': [377918376086184, 7348561, 12516744, 753220451269704, 15301704, 3, 6706022400, 6799906713600000]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{30}.(C_4\\times D_6)', 'transitive_degree': 120, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [3]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_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, 1], [4, 1, 2]], 'center_label': '4.1', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [4, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 4, 'exponents_of_order': [2], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '2.1', '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4]], 'label': '4.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C4', 'ngens': 1, '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': 3, 'number_characteristic_subgroups': 3, 'number_conjugacy_classes': 4, 'number_divisions': 3, 'number_normal_subgroups': 3, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 3, 'number_subgroups': 3, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 1], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[3]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1]], 'representations': {'PC': {'code': 5, 'gens': [1], 'pres': [2, -2, -2, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [56, 15], 'family': 'CSOPlus'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [21]}, 'Perm': {'d': 4, 'gens': [22, 7]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
