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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'ambient': '1210.10', 'ambient_counter': 10, 'ambient_order': 1210, 'ambient_tex': 'C_{11}:F_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 11, 'counter': 5, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1210.10.11.a1.a1', 'maximal': True, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '11.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 11, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '110.1', 'subgroup_hash': 1, 'subgroup_order': 110, 'subgroup_tex': 'F_{11}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1210.10', 'aut_centralizer_order': 10, 'aut_label': '11.a1', 'aut_quo_index': None, 'aut_stab_index': 22, 'aut_weyl_group': '110.1', 'aut_weyl_index': 220, 'centralizer': '1210.a1.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['22.a1.a1', '55.a1.a1', '121.a1.a1'], 'core': '110.a1.a1', 'coset_action_label': None, 'count': 11, 'diagramx': [2978, -1, 1924, -1, 7649, -1, 5123, -1], 'generators': [5, 110, 2], 'label': '1210.10.11.a1.a1', 'mobius_quo': None, 'mobius_sub': -1, 'normal_closure': '1.a1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '11.a1.a1', 'old_label': '11.a1.a1', 'projective_image': '1210.10', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '11.a1.a1', 'subgroup_fusion': None, 'weyl_group': '110.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [10, 11], 'aut_gens': [[1, 10], [21, 70], [41, 10]], 'aut_group': '110.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 110, 'aut_permdeg': 11, 'aut_perms': [1022883, 38462863], 'aut_phi_ratio': 2.75, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 11, 1, 1], [5, 11, 1, 4], [10, 11, 1, 4], [11, 10, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'F_{11}', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 11, 1], [5, 11, 4], [10, 11, 4], [11, 10, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '110.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '11.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 11, 1, 1], [5, 11, 4, 1], [10, 11, 4, 1], [11, 10, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 110, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '110.1', 'hash': 1, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11], 'inner_gens': [[1, 70], [51, 10]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 110, 'inner_split': True, 'inner_tex': 'F_{11}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 10, 'irrQ_dim': 10, 'irrR_degree': 10, 'irrep_stats': [[1, 10], [10, 1]], 'label': '110.1', 'linC_count': 1, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'F11', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, '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': 11, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 11, 'number_divisions': 5, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 38, 'old_label': None, 'order': 110, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 11], [5, 44], [10, 44], [11, 10]], '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': 2, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [10, 1]], 'representations': {'PC': {'code': 1570297039, 'gens': [1, 3], 'pres': [3, -2, -5, -11, 6, 632, 230]}, 'Lie': [{'d': 1, 'q': 11, 'gens': [462120, 4037913], 'family': 'AGL'}, {'d': 1, 'q': 11, 'gens': [462120, 4037913], 'family': 'AGammaL'}], 'GLFp': {'d': 2, 'p': 11, 'gens': [1343, 11989]}, 'Perm': {'d': 11, 'gens': [3628799, 1332490, 36288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'F_{11}', 'transitive_degree': 11, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [22, 10, 110, 11], 'aut_gens': [[1, 10, 110], [1049, 110, 10], [1051, 20, 660], [11, 10, 770], [551, 10, 110]], 'aut_group': '24200.bg', 'aut_hash': 3957277396302200749, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24200, 'aut_permdeg': 242, 'aut_perms': [128752448633818362160790012152845115067871995360975010551768033360131482115503164698929655260319547538183665881677188092802834490480727524276270369563037932167558653050009004304691542986410023185477487314309142144058226949382883115284038458888934885526573331282849266036584107311823717136487452129666762976789376271222563800551007614901286727006032378398303970392681665179209750709821414957415305171392082047891294386313927422055132540035112291197784286836992029106873287742, 58811990310190613105397047279932204955380287640061730511247281961248574489325117663338475226215917128324817962195613609683643064858349661372163501734819189918672041937401859193702488265397363123438435972781792561949254719508902523317629185860103572214099678218147442632955060457646100412870470664590803634086368649869681288085473649655083301055869349459682903063466201251555222863376532585315747614860392014937542494364227315880435784036266533812387163399922684268383573192, 116918878992687092125980870420335873430636166584677098658384915169064683419034329733926808805779564206497265784286302599409181697872771966466177250963026191866278782320054349383541144941507224981629244987126025222179034650368028933168530832349939056125690316490950292113738124398259762398356606604909519530111499358388125306158665990635314756171128994253809665503285158103318135483124338990946311169791861906636351981101509343729869082325808145116311987913657920906406863306, 223949079963832821347897113073396041609480111836341491414313111222999879561003990832654990327802884169105423825064179742629453293652733513523427250561564792494895532942571316474916904771432017639892764495547973823512560560947262008968680225174954994228967906572330083248035603170420862148509536985336337140653287886053171884786000581980268590734590766367637530217349668335723196008647420988172332043911458250844267259023961911872350750534542776449232656897113328803860027781], 'aut_phi_ratio': 55.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 2, 2], [10, 121, 2, 2], [11, 10, 2, 1], [11, 10, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}\\wr C_2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 121, 1], [5, 121, 4], [10, 121, 4], [11, 10, 12]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1210.10', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '5.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 10, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 121, 1, 1], [5, 121, 4, 1], [10, 121, 4, 1], [11, 10, 1, 2], [11, 10, 5, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 36, 'exponent': 110, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 10]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1210.10', 'hash': 10, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11, 11], 'inner_gens': [[1, 70, 880], [51, 10, 110], [441, 10, 110]], 'inner_hash': 10, 'inner_nilpotent': False, 'inner_order': 1210, 'inner_split': False, 'inner_tex': 'C_{11}:F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 10, 'irrQ_degree': 50, 'irrQ_dim': 50, 'irrR_degree': 10, 'irrep_stats': [[1, 10], [10, 12]], 'label': '1210.10', 'linC_count': 10, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 10, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11:F11', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 22, 'number_divisions': 8, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 14, 'number_subgroup_classes': 20, 'number_subgroups': 556, 'old_label': None, 'order': 1210, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 121], [5, 484], [10, 484], [11, 120]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [6, 5], 'outer_gens': [[1, 90, 660], [9, 660, 10]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [720, 41081], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2], [10, 2], [50, 2]], 'representations': {'PC': {'code': 88200547802529130399, 'gens': [1, 3, 4], 'pres': [4, -2, -5, -11, -11, 8, 842, 306, 14083, 7927]}, 'GLFp': {'d': 3, 'p': 11, 'gens': [2143604792, 295918632, 1103176378, 418103038]}, 'Perm': {'d': 22, 'gens': [2446779061503273623, 5251477993144647437, 4738577, 58410722688808089600]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}:F_{11}', 'transitive_degree': 55, 'wreath_data': None, 'wreath_product': False}
