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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '319440.x', 'ambient_counter': 24, 'ambient_order': 319440, 'ambient_tex': 'C_{11}^3:(C_{10}\\times D_{12})', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 13310, 'counter': 77, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '319440.x.24._.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '24.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '24.6', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 24, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_{12}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '13310.bv', 'subgroup_hash': None, 'subgroup_order': 13310, 'subgroup_tex': 'C_{11}^3:C_{10}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '319440.x', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [43718074150397584, 4622959461834174, 37595466963011736, 7061686783493871, 5356356801680985], 'label': '319440.x.24._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '24.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '24._.C', 'subgroup_fusion': None, 'weyl_group': None}
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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': 1, 'aut_exponent': 175560, 'aut_gen_orders': [2660, 10, 30], 'aut_gens': [[1, 10, 110, 1210], [6893, 1550, 4030, 13100], [12829, 80, 280, 9620], [9019, 1370, 3200, 3870]], 'aut_group': None, 'aut_hash': 3405692464592397592, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11309645424000, 'aut_permdeg': 1335, 'aut_perms': 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'aut_phi_ratio': 2336703600.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1331, 1, 1], [5, 1, 4, 1], [10, 1331, 4, 1], [11, 2, 665, 1], [55, 2, 2660, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4\\times C_{11}^3.C_{10}.\\PSL(3,11)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 175560, 'autcentquo_group': None, 'autcentquo_hash': 4977165058291360190, 'autcentquo_nilpotent': False, 'autcentquo_order': 2827411356000, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^3.C_{10}.\\PSL(3,11)', 'cc_stats': [[1, 1, 1], [2, 1331, 1], [5, 1, 4], [10, 1331, 4], [11, 2, 665], [55, 2, 2660]], 'center_label': '5.1', 'center_order': 5, 'central_product': True, 'central_quotient': '2662.12', 'commutator_count': 1, 'commutator_label': '1331.5', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 48, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2662.12', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1331, 1, 1], [5, 1, 4, 1], [10, 1331, 4, 1], [11, 2, 5, 133], [55, 2, 20, 133]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2340, 'exponent': 110, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 5, 7, 11, 19], 'factors_of_order': [2, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '13310.bv', 'hash': 3094167567471054012, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [2, 11, 11, 11], 'inner_gens': [[1, 100, 1100, 12100], [21, 10, 110, 1210], [221, 10, 110, 1210], [2421, 10, 110, 1210]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 2662, 'inner_split': True, 'inner_tex': 'C_{11}^3:C_2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': None, 'irrep_stats': [[1, 10], [2, 3325]], 'label': '13310.bv', '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': 'C11^3:C10', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 3335, 'number_divisions': 270, 'number_normal_subgroups': 538, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 1072, 'number_subgroups': 38312, 'old_label': None, 'order': 13310, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 1331], [5, 4], [10, 5324], [11, 1330], [55, 5320]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 175560, 'outer_gen_orders': [532, 1330], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 5330, 12840, 1070], [9, 1850, 2120, 2320]], 'outer_group': None, 'outer_hash': 4009647696620411150, 'outer_nilpotent': False, 'outer_order': 4248552000, 'outer_permdeg': 142, 'outer_perms': [21915043435026896782159260352298638765894793732063781672029769076217294086660934603415049024986867319086214735014348031960739682294206853883750597446497979477348823865190090949811646353517368857014522080856740983221256853610419858677454139168009, 164009035136120551564590284182003334369357930995268334710127851998166877715290581503247061531384225266174894324848626575893558306325486518180980344632852739867184643969169015392770187500789946601034706664221690272508151795600504673277096847842576], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_{20}\\times \\PSL(3,11)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 38, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [4, 2], [10, 133], [40, 133]], 'representations': {'PC': {'code': '34798112225396348903999', 'gens': [1, 3, 4, 5], 'pres': [5, -2, -5, -11, -11, -11, 10, 1502, 22003, 302504]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 41725369603789104, 44509179942611006, 1977210383605740, 36687300164533435]}, 'Perm': {'d': 38, 'gens': [14879759122079716194687946629899895124838446, 63, 372289110536814240177545247145793091529517, 27538430075611354098608948951783797146470463, 42067131891856665007034158202550831861898188]}}, 'schur_multiplier': [11, 11, 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}^3:C_{10}', 'transitive_degree': 6655, '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': '40.14', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[35715392747806643, 19063078487671420, 3519921862562674, 17298483428108842, 45842145882403683, 41608089875869718, 12531822321003912, 33418192856010432, 4764541194236758], [35564740259935813, 18946948711944521, 30612033140022726, 16502600281671387, 34040965705109643, 37165754801746531, 12531822321003912, 33418192856010432, 3973183186977819], [35715392747806643, 19063078487671420, 4870457795763859, 22951256970770724, 1181466045481482, 6874134118865165, 12531822321003912, 33418192856010432, 17475997798440211], [20539705140219756, 3887105568413922, 19874692145181020, 19155564770985712, 1555446791673916, 37165754801746531, 12531822321003912, 33418192856010432, 21271430602705840], [35715392747806643, 19063078487671420, 3519921862562674, 17298483428108842, 45842145882403683, 41608089875869718, 12531822321003912, 33418192856010432, 4764541194236758], [35715392747806643, 19063078487671420, 3519921862562674, 17298483428108842, 45842145882403683, 41608089875869718, 12531822321003912, 33418192856010432, 4764541194236758], [26152754368917588, 9120376668156221, 29432440190671409, 22951256970770724, 19620317354834069, 30489729317839423, 12531822321003912, 33418192856010432, 27418699635685661], [23654314194561672, 19063078487671420, 3519921862562674, 17298483428108842, 25957053260218303, 39935675520312130, 12531822321003912, 33418192856010432, 4764541194236758], [30595061147653963, 19063078487671420, 1016251838993157, 17298483428108842, 39011673831712076, 36139105057878574, 12531822321003912, 33418192856010432, 4764541194236758], [34390493953691153, 19063078487671420, 32433744327791203, 17298483428108842, 2507719367478906, 39934511926491163, 12531822321003912, 33418192856010432, 4764541194236758], [1149082265945834, 30480735269856092, 36229176919484153, 16801134840411034, 5772623004182094, 32346810680217984, 12531822321003912, 33418192856010432, 38155218892913015], [33892126636285635, 17239527064479801, 8754221728460728, 42568624234005174, 3686988505511065, 18953903158374654, 12531822321003912, 33418192856010432, 30035389480921159], [24184459519204595, 7532145259069372, 32434591790418528, 25565826899594807, 14265458779092270, 44589234511166488, 12531822321003912, 33418192856010432, 5296018809406952], [26359958017282609, 7532145259069372, 32434591790418528, 25565826899594807, 36279243854706664, 5955442401338276, 12531822321003912, 33418192856010432, 5296018809406952], [6735663244327742, 23596485072782074, 42582086064442726, 9914453460290471, 6171648344656957, 37273298901009897, 20886370535006520, 25063644642007824, 15090864729501011], [19594895668738452, 10977774126138813, 43595709749380329, 14476054218388935, 29841011746899935, 9196140234579193, 16709096428005216, 29240918749009128, 31390550493308157]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 51110400, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 2, 1], [2, 726, 2, 1], [2, 1331, 2, 1], [3, 242, 1, 1], [4, 22, 1, 1], [4, 242, 1, 1], [5, 1, 4, 1], [6, 242, 1, 1], [6, 2662, 2, 1], [10, 1, 4, 1], [10, 66, 8, 1], [10, 726, 8, 1], [10, 1331, 8, 1], [11, 2, 5, 1], [11, 6, 10, 1], [11, 12, 5, 1], [11, 12, 50, 1], [11, 24, 25, 1], [12, 242, 2, 1], [12, 2662, 2, 1], [15, 242, 4, 1], [20, 22, 4, 1], [20, 242, 4, 1], [22, 2, 5, 1], [22, 6, 10, 1], [22, 12, 5, 1], [22, 12, 50, 1], [22, 24, 25, 1], [22, 132, 10, 2], [22, 132, 100, 1], [22, 1452, 10, 1], [30, 242, 4, 1], [30, 2662, 8, 1], [33, 484, 5, 1], [44, 132, 10, 2], [44, 484, 5, 1], [55, 2, 20, 1], [55, 6, 40, 1], [55, 12, 20, 1], [55, 12, 200, 1], [55, 24, 100, 1], [60, 242, 8, 1], [60, 2662, 8, 1], [66, 484, 5, 1], [110, 2, 20, 1], [110, 6, 40, 1], [110, 12, 20, 1], [110, 12, 200, 1], [110, 24, 100, 1], [110, 132, 40, 2], [110, 132, 400, 1], [110, 1452, 40, 1], [132, 484, 10, 1], [165, 484, 20, 1], [220, 132, 40, 2], [220, 484, 20, 1], [330, 484, 20, 1], [660, 484, 40, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 66, 2], [2, 726, 2], [2, 1331, 2], [3, 242, 1], [4, 22, 1], [4, 242, 1], [5, 1, 4], [6, 242, 1], [6, 2662, 2], [10, 1, 4], [10, 66, 8], [10, 726, 8], [10, 1331, 8], [11, 2, 5], [11, 6, 10], [11, 12, 55], [11, 24, 25], [12, 242, 2], [12, 2662, 2], [15, 242, 4], [20, 22, 4], [20, 242, 4], [22, 2, 5], [22, 6, 10], [22, 12, 55], [22, 24, 25], [22, 132, 120], [22, 1452, 10], [30, 242, 4], [30, 2662, 8], [33, 484, 5], [44, 132, 20], [44, 484, 5], [55, 2, 20], [55, 6, 40], [55, 12, 220], [55, 24, 100], [60, 242, 8], [60, 2662, 8], [66, 484, 5], [110, 2, 20], [110, 6, 40], [110, 12, 220], [110, 24, 100], [110, 132, 480], [110, 1452, 40], [132, 484, 10], [165, 484, 20], [220, 132, 80], [220, 484, 20], [330, 484, 20], [660, 484, 40]], 'center_label': '10.2', 'center_order': 10, 'central_product': None, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '7986.b', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 9, 'conjugacy_classes_known': False, 'counter': 24, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 66, 1, 2], [2, 726, 1, 2], [2, 1331, 1, 2], [3, 242, 1, 1], [4, 22, 1, 1], [4, 242, 1, 1], [5, 1, 4, 1], [6, 242, 1, 1], [6, 2662, 1, 2], [10, 1, 4, 1], [10, 66, 4, 2], [10, 726, 4, 2], [10, 1331, 4, 2], [11, 2, 5, 1], [11, 6, 5, 2], [11, 12, 5, 11], [11, 24, 5, 5], [12, 242, 2, 1], [12, 2662, 2, 1], [15, 242, 4, 1], [20, 22, 4, 1], [20, 242, 4, 1], [22, 2, 5, 1], [22, 6, 5, 2], [22, 12, 5, 11], [22, 24, 5, 5], [22, 132, 5, 24], [22, 1452, 5, 2], [30, 242, 4, 1], [30, 2662, 4, 2], [33, 484, 5, 1], [44, 132, 5, 2], [44, 132, 10, 1], [44, 484, 5, 1], [55, 2, 20, 1], [55, 6, 20, 2], [55, 12, 20, 11], [55, 24, 20, 5], [60, 242, 8, 1], [60, 2662, 8, 1], [66, 484, 5, 1], [110, 2, 20, 1], [110, 6, 20, 2], [110, 12, 20, 11], [110, 24, 20, 5], [110, 132, 20, 24], [110, 1452, 20, 2], [132, 484, 10, 1], [165, 484, 20, 1], [220, 132, 20, 2], [220, 132, 40, 1], [220, 484, 20, 1], [330, 484, 20, 1], [660, 484, 40, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 660, 'exponents_of_order': [4, 3, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[12, 0, 400], [24, 0, 100]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 4185823851600239521, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 31944, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': 12, 'irrQ_degree': 240, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 40], [2, 150], [4, 125], [6, 200], [12, 1150], [24, 250]], 'label': '319440.x', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C11^3:(C10*D12)', 'ngens': 9, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 3, 1, 0, 1, 0, 3, 1, 1, 1, 0, 3, 0, 1, 3, 3, 0, 1, 3, 1, 7, 1, 0, 3, 0, 7, 3, 1, 1, 7, 0, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 64, 'number_characteristic_subgroups': 54, 'number_conjugacy_classes': 1915, 'number_divisions': 174, 'number_normal_subgroups': 82, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 319440, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 4247], [3, 242], [4, 264], [5, 4], [6, 5566], [10, 16988], [11, 1330], [12, 5808], [15, 968], [20, 1056], [22, 31690], [30, 22264], [33, 2420], [44, 5060], [55, 5320], [60, 23232], [66, 2420], [110, 126760], [132, 4840], [165, 9680], [220, 20240], [330, 9680], [660, 19360]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '1600.9725', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 1600, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_4^2:C_{10}^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 53, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 6], [4, 10], [8, 6], [10, 4], [16, 2], [20, 3], [30, 8], [40, 5], [60, 44], [80, 3], [120, 19], [160, 1], [240, 44], [480, 11]], 'representations': {'PC': {'code': '1052856233766732433237675855687326067142310701469027458468355603583007084539484946945180735498283858164987330433596180720808438545138753535541030900199', 'gens': [1, 3, 5, 8, 9], 'pres': [9, -2, -5, -2, -11, -2, -2, -3, -11, 11, 18, 3926072, 74, 7203, 2148304, 1068232, 83686, 130, 6866645, 539375, 143780, 158, 10699926, 826080, 992409, 1900807, 90763, 44980, 5893, 23522408, 2352266, 73916, 31643, 13670]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [35715392747806643, 19063078487671420, 3519921862562674, 17298483428108842, 45842145882403683, 41608089875869718, 12531822321003912, 33418192856010432, 4764541194236758]}, 'Perm': {'d': 53, 'gens': [90153581084939059608260573105376257375173290945031274148945189568223, 2889816652800, 172449869891412836091442928440406949365273195890681624273935925507324, 251555002641641925793755298194142521301321426698085407686362564548866, 122003677653580800, 335134112179633897906986081465545605165048026154912430962776210962827, 404846876183785111435375840910340253070913926877650843474383497672376, 10985012109560724119573357411371438194049572430424672610431824385174, 498216305262746722318331122824386819374027122828493771080605607393976]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 10], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 2904, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_{11}^3:(C_{10}\\times D_{12})', 'transitive_degree': 660, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 12], 'aut_gens': [[1, 2], [1, 10], [1, 14], [15, 2]], 'aut_group': '48.38', 'aut_hash': 38, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 7, 'aut_perms': [745, 24, 1707], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 2, 1], [3, 2, 1, 1], [4, 2, 1, 1], [6, 2, 1, 1], [12, 2, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3\\times D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '12.4', 'autcentquo_hash': 4, 'autcentquo_nilpotent': False, 'autcentquo_order': 12, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 6, 2], [3, 2, 1], [4, 2, 1], [6, 2, 1], [12, 2, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 6, 1, 2], [3, 2, 1, 1], [4, 2, 1, 1], [6, 2, 1, 1], [12, 2, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 3, 'exponent': 12, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[2, 1, 2]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '12.4', 'hash': 6, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6], 'inner_gens': [[1, 22], [5, 2]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': True, 'inner_tex': 'D_6', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 5]], 'label': '24.6', 'linC_count': 2, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 3, 'linQ_dim': 4, 'linQ_dim_count': 3, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'D12', 'ngens': 4, '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': 7, 'number_characteristic_subgroups': 7, 'number_conjugacy_classes': 9, 'number_divisions': 8, 'number_normal_subgroups': 9, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 16, 'number_subgroups': 34, 'old_label': None, 'order': 24, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 13], [3, 2], [4, 2], [6, 2], [12, 4]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [6, 0], 'outer_gens': [[7, 2], [1, 14]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 3], [4, 1]], 'representations': {'PC': {'code': 2968216545, 'gens': [1, 2], 'pres': [4, -2, -2, -2, -3, 177, 21, 242, 34, 259]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [1381251, 40593880]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [11822, 13311]}, 'Perm': {'d': 7, 'gens': [745, 1464, 2424, 3]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{12}', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
