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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': True, 'core_order': 15972, 'counter': 59, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '319440.x.20._.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '15972.m', 'subgroup_hash': None, 'subgroup_order': 15972, 'subgroup_tex': 'C_{11}^3:C_{12}', 'supersolvable': False, '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, 25577585254323209, 15010694499031600, 42302886394817014, 7061686783493871, 5356356801680985], 'label': '319440.x.20._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '20.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '20._.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': '12.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [12, 60, 2, 20, 30], 'aut_gens': [[1, 12, 132, 1452], [7861, 120, 10824, 396], [6511, 72, 8712, 3036], [5951, 120, 5016, 9108], [1145, 120, 3564, 9372], [8941, 84, 9504, 11748]], 'aut_group': None, 'aut_hash': 8081849349039815596, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6388800, 'aut_permdeg': 264, 'aut_perms': 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10643050046852291375260812672242655648824451526636447979468336351853111330172739160894606982209663092510549698075259734339908465700793482741165036909792504995479533345878314361616027015953514931324248649137190001240239788926045564864282037673017395219193139455240171964814361131402902736933320657637415721497151169054971019603679865528181547152401852711107745576677784890882467597206221104767875093477002070381083108638759089101482913066741853696115262971166325896905408134728787681526090575337651070562377801923424550080391069, 2999199143860142561359596293294226256951713914923031203052771130892400799195695668146851745100142243683157637117440325804338550222168156442695903611522952760438813212339483210601935238713483842869906159995023312750101299496454326270118632601954427914081479807387197020372793410323984130349225477445134692437806226599562193317186934189024660362561131213633889217946871246194967474323419667206370599225891942249585614469425311160327073473578938765223721528356650876690598360334158429837106273741352994530653477758673451627920192, 1831656114052285046753113996530985222845891031822089770406273335403291964396723191911469719606464237319802696163604230774293514896805699546167491497549259217757108052031600426510101596532024959744727088952766374575636245574047446294571173249521421651685213443235839840060851737981762461620769228218832068199094294495297940594712349802715472202774550682662889640347827572276971065160588970951960536869880926162422366755994676229750988686899215579745333954006029816191022282793050450950606256466662546447758549041499937717982866], 'aut_phi_ratio': 1320.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 121, 2, 1], [4, 11, 2, 1], [6, 121, 2, 1], [11, 2, 5, 1], [11, 3, 40, 1], [11, 6, 200, 1], [12, 1331, 4, 1], [22, 2, 5, 1], [22, 3, 40, 1], [22, 6, 200, 1], [33, 242, 10, 1], [44, 33, 80, 1], [66, 242, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^3.C_{60}.C_5.C_2^4', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': None, 'autcentquo_hash': 5378863073839833794, 'autcentquo_nilpotent': False, 'autcentquo_order': 3194400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^3.C_{60}.C_5.C_2^3', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 121, 2], [4, 11, 2], [6, 121, 2], [11, 2, 5], [11, 3, 40], [11, 6, 200], [12, 1331, 4], [22, 2, 5], [22, 3, 40], [22, 6, 200], [33, 242, 10], [44, 33, 80], [66, 242, 10]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '1331.5', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '3.1', '11.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['363.2', 1], ['44.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 121, 2, 1], [4, 11, 2, 1], [6, 121, 2, 1], [11, 2, 5, 1], [11, 3, 10, 4], [11, 6, 10, 20], [12, 1331, 4, 1], [22, 2, 5, 1], [22, 3, 10, 4], [22, 6, 10, 20], [33, 242, 10, 1], [44, 33, 20, 4], [66, 242, 10, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 132, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[6, 0, 200]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 5173332969165016753, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [6, 11, 11, 11], 'inner_gens': [[1, 120, 3036, 13596], [25, 12, 132, 1452], [13069, 12, 132, 1452], [5281, 12, 132, 1452]], 'inner_hash': 7345092711346113254, 'inner_nilpotent': False, 'inner_order': 7986, 'inner_split': True, 'inner_tex': 'C_{11}^3:C_6', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 60, 'irrQ_dim': 60, 'irrR_degree': None, 'irrep_stats': [[1, 12], [2, 30], [3, 160], [6, 400]], 'label': '15972.m', '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:C12', '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': 15, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 602, 'number_divisions': 62, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 34, 'number_subgroup_classes': 128, 'number_subgroups': 2656, 'old_label': None, 'order': 15972, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 242], [4, 22], [6, 242], [11, 1330], [12, 5324], [22, 1330], [33, 2420], [44, 2640], [66, 2420]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 40, 'outer_gen_orders': [2, 10, 40], 'outer_gen_pows': [0, 0, 4], 'outer_gens': [[7, 12, 132, 1452], [11, 108, 12672, 5016], [7, 120, 11484, 7656]], 'outer_group': '800.952', 'outer_hash': 952, 'outer_nilpotent': True, 'outer_order': 800, 'outer_permdeg': 20, 'outer_perms': [39916800, 13516128494668864, 878906256402182433], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_8:C_{10}^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 48, 'pgroup': 0, 'primary_abelian_invariants': [4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 3], [4, 1], [10, 2], [20, 2], [30, 8], [60, 44]], 'representations': {'PC': {'code': '230929128943843892733216827706998384604035001999', 'gens': [1, 4, 5, 6], 'pres': [6, -2, -2, -3, -11, -11, 11, 12, 31, 2883, 91084, 213850, 22786, 489461, 42779, 122381]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [41360875880200184, 41636115214472921, 25272377535819489, 39770602361819421, 7061686783493871, 41772741070013040]}, 'Perm': {'d': 48, 'gens': [286748360502225383946947392227296050142180776796558804908329, 550999224819542438169252483709073112714395140098916526787360, 815369168730937142505730909362468854549173300286881955563080, 1079617868315636983432163082162649586673314075438446591723080, 1304369293652518592298715430010697649088447858132137934369856, 16]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [12], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^3:C_{12}', 'transitive_degree': 132, '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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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12], 'aut_gens': [[1, 2], [10, 13], [10, 15]], 'aut_group': '24.5', 'aut_hash': 5, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [127, 857], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [10, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.5', 'autcent_hash': 5, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times 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], [5, 1, 4], [10, 1, 12]], 'center_label': '20.5', 'center_order': 20, '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', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [10, 1, 4, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20.5', 'hash': 5, '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, 20]], 'label': '20.5', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 6, 'linQ_dim': 5, 'linQ_dim_count': 6, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C10', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [5, 4], [10, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[10, 13], [10, 15]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [127, 857], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4]], 'representations': {'PC': {'code': 2179, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 16]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706303489327]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [13320, 4001]}, 'Perm': {'d': 9, 'gens': [40320, 720, 96]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{10}', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
