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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1584.318', 'ambient_counter': 318, 'ambient_order': 1584, 'ambient_tex': 'D_{66}:C_{12}', 'central': True, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 1, 'counter': 152, 'cyclic': True, 'direct': True, 'hall': 1, 'label': '1584.318.1584.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1584.a1.a1', 'outer_equivalence': False, 'perfect': True, 'proper': False, 'quotient': '1584.318', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 318, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 1584, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{66}:C_{12}', 'simple': False, 'solvable': True, 'special_labels': ['PC', 'U2', 'D2', 'C7'], 'split': True, 'standard_generators': False, 'stem': True, 'subgroup': '1.1', 'subgroup_hash': 1, 'subgroup_order': 1, 'subgroup_tex': 'C_1', 'supersolvable': True, 'sylow': 1}
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gps_subgroup_data • Show schema
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{'ambient': '1584.318', 'aut_centralizer_order': None, 'aut_label': '1584.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1.a1', 'complements': ['1.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '528.a1.a1', '528.b1.a1', '528.c1.a1', '792.a1.a1', '792.b1.a1', '792.c1.a1', '792.d1.a1', '792.d1.b1'], 'contains': [], 'core': '1584.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3105, 6981, 3644, 3431, 2445, 4613, 4509, 3821], 'generators': [], 'label': '1584.318.1584.a1.a1', 'mobius_quo': 1, 'mobius_sub': 0, 'normal_closure': '1584.a1.a1', 'normal_contained_in': ['144.a1.a1', '528.a1.a1', '528.b1.a1', '792.c1.a1', '792.b1.a1', '792.a1.a1'], 'normal_contains': [], 'normalizer': '1.a1.a1', 'old_label': '1584.a1.a1', 'projective_image': '1584.318', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1584.a1.a1', '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': '1.1', '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': [], '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]], '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]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': [], 'composition_length': 0, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1, 'exponent': 1, 'exponents_of_order': [], 'factors_of_aut_order': [], 'factors_of_order': [], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '1.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [], 'inner_gens': [], '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, 1]], 'label': '1.1', 'linC_count': 1, 'linC_degree': 0, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 0, 'linQ_degree_count': 1, 'linQ_dim': 0, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 0, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C1', 'ngens': 0, 'nilpotency_class': 0, 'nilpotent': True, 'normal_counts': [1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1, 'number_characteristic_subgroups': 1, 'number_conjugacy_classes': 1, 'number_divisions': 1, 'number_normal_subgroups': 1, 'number_subgroup_autclasses': 1, 'number_subgroup_classes': 1, 'number_subgroups': 1, 'old_label': None, 'order': 1, 'order_factorization_type': 0, 'order_stats': [[1, 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': 0, 'perfect': True, 'permutation_degree': 1, 'pgroup': 1, 'primary_abelian_invariants': [], 'quasisimple': False, 'rank': 0, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 1]], 'representations': {'PC': {'code': 0, 'gens': [], 'pres': []}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_1', 'transitive_degree': 1, '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': 330, 'aut_gen_orders': [10, 6, 66, 30, 30, 10, 10, 10], 'aut_gens': [[1, 2, 12], [697, 10, 1434], [559, 2, 1314], [1255, 2, 18], [991, 10, 948], [553, 10, 1524], [1351, 2, 708], [673, 10, 1290], [649, 10, 60]], 'aut_group': None, 'aut_hash': 3218128654472875310, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 138, 'aut_perms': [358428707339722190394435771473186532531842484154961468647040272423122427906627278204230774068626290494152789807645644322406865471009074102422512607472798478745872362704548450287536586479781896079804729620211147363745877399805352366738936, 28975334910074185206280676148762955498790448883979209565133280768963243675418414370038192981034733070739522609142270677180134836650195515609860632920311849070164261154984760313603951333933605775621788831981232933518834149297965106559565, 97066378814085514316192783946266463048256236337048965242465466963895263440127288727491080995501993311673959915799109203346662388209812893929898254239321623650911756812825530698414121970983798782954305915870650303017752860645581719818861, 574949222561319905543485320402064963434609030586717218151176410952641345383763525347400736850212729971349771130739469423429076687984483226187575737996542911308330073742249166099006104702660779953420512330295057543788875965300490427426666, 336941070288613261953544682678469209382917045695662069213246132034762846259786436219636371852195287235006644171454764572800011293222552473660303080522144352458545805562383787573104358747766684156904397839861820663848358000174146635556502, 57737788143757967046714787841533182501030951981739070408200480439937441068914901157837982328966786392569655525118891897115921164812128236040642755672320516187433779140316711932874916459611469637892847302297891653654589753074412621492357, 476301782808822969179660327933756719584353990040367605519854797749378081898438703873030109121898813534019654115872932986364900476111015028848584311104039858592717080107831829232606497901833056580199441770010409360357089628339618686975998, 349846146236029277506941545882117958291443839150765370812637284556242817617463369143746874384164594001424193216987739481684113848645867708992901731076269236989262444981512287132334993963619727440786785349241800810794649919342047720810571], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 66, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 2, 1], [4, 66, 2, 1], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 66, 4, 1], [11, 2, 5, 1], [12, 2, 4, 2], [12, 2, 8, 1], [12, 66, 4, 1], [22, 2, 5, 3], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 20, 1], [66, 2, 10, 6], [66, 2, 20, 3], [132, 2, 40, 2], [132, 2, 80, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times C_{11}:C_5).C_2^6', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 66, 2], [3, 1, 2], [3, 2, 3], [4, 2, 2], [4, 66, 2], [6, 1, 6], [6, 2, 9], [6, 66, 4], [11, 2, 5], [12, 2, 16], [12, 66, 4], [22, 2, 15], [33, 2, 40], [44, 2, 20], [66, 2, 120], [132, 2, 160]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '132.9', 'commutator_count': 1, 'commutator_label': '66.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 318, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['528.73', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 66, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 2, 1], [4, 66, 2, 1], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 66, 2, 2], [11, 2, 5, 1], [12, 2, 4, 4], [12, 66, 4, 1], [22, 2, 5, 3], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 20, 1], [66, 2, 10, 6], [66, 2, 20, 3], [132, 2, 40, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 132, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '396.27', 'hash': 318, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 1, 66], 'inner_gens': [[1, 2, 786], [1, 2, 12], [823, 2, 12]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'D_{66}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 390]], 'label': '1584.318', 'linC_count': 1280, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 12, 'linQ_dim': 16, 'linQ_dim_count': 12, 'linR_count': 80, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D66:C12', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 414, 'number_divisions': 48, 'number_normal_subgroups': 58, 'number_subgroup_autclasses': 134, 'number_subgroup_classes': 152, 'number_subgroups': 1536, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 135], [3, 8], [4, 136], [6, 288], [11, 10], [12, 296], [22, 30], [33, 80], [44, 40], [66, 240], [132, 320]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 2, 10], 'outer_gen_pows': [1056, 0, 0, 0, 528], 'outer_gens': [[1057, 2, 1308], [1, 2, 780], [793, 2, 1308], [1, 2, 516], [1057, 10, 876]], 'outer_group': '160.238', 'outer_hash': 238, 'outer_nilpotent': True, 'outer_order': 160, 'outer_permdeg': 15, 'outer_perms': [720, 87178291200, 479001600, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 11], [8, 2], [10, 2], [20, 7], [40, 10], [80, 2]], 'representations': {'PC': {'code': 302676377150983156657325070129220010019, 'gens': [1, 2, 4], 'pres': [7, 2, 2, 3, 2, 2, 3, 11, 36, 22011, 80, 54604, 102, 64517, 166, 70566]}, 'Perm': {'d': 25, 'gens': [25903229683152680046725, 8023689, 840, 3669136, 16, 6706022400, 672254861098236159744000]}}, 'schur_multiplier': [2, 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': 'D_{66}:C_{12}', 'transitive_degree': 528, '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': 330, 'aut_gen_orders': [10, 6, 66, 30, 30, 10, 10, 10], 'aut_gens': [[1, 2, 12], [697, 10, 1434], [559, 2, 1314], [1255, 2, 18], [991, 10, 948], [553, 10, 1524], [1351, 2, 708], [673, 10, 1290], [649, 10, 60]], 'aut_group': None, 'aut_hash': 3218128654472875310, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 21120, 'aut_permdeg': 138, 'aut_perms': [358428707339722190394435771473186532531842484154961468647040272423122427906627278204230774068626290494152789807645644322406865471009074102422512607472798478745872362704548450287536586479781896079804729620211147363745877399805352366738936, 28975334910074185206280676148762955498790448883979209565133280768963243675418414370038192981034733070739522609142270677180134836650195515609860632920311849070164261154984760313603951333933605775621788831981232933518834149297965106559565, 97066378814085514316192783946266463048256236337048965242465466963895263440127288727491080995501993311673959915799109203346662388209812893929898254239321623650911756812825530698414121970983798782954305915870650303017752860645581719818861, 574949222561319905543485320402064963434609030586717218151176410952641345383763525347400736850212729971349771130739469423429076687984483226187575737996542911308330073742249166099006104702660779953420512330295057543788875965300490427426666, 336941070288613261953544682678469209382917045695662069213246132034762846259786436219636371852195287235006644171454764572800011293222552473660303080522144352458545805562383787573104358747766684156904397839861820663848358000174146635556502, 57737788143757967046714787841533182501030951981739070408200480439937441068914901157837982328966786392569655525118891897115921164812128236040642755672320516187433779140316711932874916459611469637892847302297891653654589753074412621492357, 476301782808822969179660327933756719584353990040367605519854797749378081898438703873030109121898813534019654115872932986364900476111015028848584311104039858592717080107831829232606497901833056580199441770010409360357089628339618686975998, 349846146236029277506941545882117958291443839150765370812637284556242817617463369143746874384164594001424193216987739481684113848645867708992901731076269236989262444981512287132334993963619727440786785349241800810794649919342047720810571], 'aut_phi_ratio': 44.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 66, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 2, 1], [4, 66, 2, 1], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 66, 4, 1], [11, 2, 5, 1], [12, 2, 4, 2], [12, 2, 8, 1], [12, 66, 4, 1], [22, 2, 5, 3], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 20, 1], [66, 2, 10, 6], [66, 2, 20, 3], [132, 2, 40, 2], [132, 2, 80, 1]], 'aut_supersolvable': True, 'aut_tex': '(C_6\\times C_{11}:C_5).C_2^6', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 66, 2], [3, 1, 2], [3, 2, 3], [4, 2, 2], [4, 66, 2], [6, 1, 6], [6, 2, 9], [6, 66, 4], [11, 2, 5], [12, 2, 16], [12, 66, 4], [22, 2, 15], [33, 2, 40], [44, 2, 20], [66, 2, 120], [132, 2, 160]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '132.9', 'commutator_count': 1, 'commutator_label': '66.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 318, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['528.73', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 66, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 2, 1], [4, 66, 2, 1], [6, 1, 2, 3], [6, 2, 1, 3], [6, 2, 2, 3], [6, 66, 2, 2], [11, 2, 5, 1], [12, 2, 4, 4], [12, 66, 4, 1], [22, 2, 5, 3], [33, 2, 10, 2], [33, 2, 20, 1], [44, 2, 20, 1], [66, 2, 10, 6], [66, 2, 20, 3], [132, 2, 40, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 132, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '396.27', 'hash': 318, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [2, 1, 66], 'inner_gens': [[1, 2, 786], [1, 2, 12], [823, 2, 12]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'D_{66}', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 390]], 'label': '1584.318', 'linC_count': 1280, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 12, 'linQ_dim': 16, 'linQ_dim_count': 12, 'linR_count': 80, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D66:C12', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 44, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 414, 'number_divisions': 48, 'number_normal_subgroups': 58, 'number_subgroup_autclasses': 134, 'number_subgroup_classes': 152, 'number_subgroups': 1536, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 135], [3, 8], [4, 136], [6, 288], [11, 10], [12, 296], [22, 30], [33, 80], [44, 40], [66, 240], [132, 320]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 2, 2, 2, 10], 'outer_gen_pows': [1056, 0, 0, 0, 528], 'outer_gens': [[1057, 2, 1308], [1, 2, 780], [793, 2, 1308], [1, 2, 516], [1057, 10, 876]], 'outer_group': '160.238', 'outer_hash': 238, 'outer_nilpotent': True, 'outer_order': 160, 'outer_permdeg': 15, 'outer_perms': [720, 87178291200, 479001600, 3628800, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 10], [4, 11], [8, 2], [10, 2], [20, 7], [40, 10], [80, 2]], 'representations': {'PC': {'code': 302676377150983156657325070129220010019, 'gens': [1, 2, 4], 'pres': [7, 2, 2, 3, 2, 2, 3, 11, 36, 22011, 80, 54604, 102, 64517, 166, 70566]}, 'Perm': {'d': 25, 'gens': [25903229683152680046725, 8023689, 840, 3669136, 16, 6706022400, 672254861098236159744000]}}, 'schur_multiplier': [2, 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': 'D_{66}:C_{12}', 'transitive_degree': 528, 'wreath_data': None, 'wreath_product': False}
