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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': 79860, 'counter': 12, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '319440.x.4._.C', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '79860.m', 'subgroup_hash': None, 'subgroup_order': 79860, 'subgroup_tex': 'C_{11}^3:C_{60}', '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, 19873046429574247, 37595466963011736, 42302886394817014, 7061686783493871, 5356356801680985], 'label': '319440.x.4._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4._.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': '60.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [20, 40, 120, 10, 220, 20], 'aut_gens': [[1, 60, 660, 7260], [69929, 2580, 780, 65340], [46393, 3240, 4740, 50820], [77671, 6420, 3240, 29040], [55771, 300, 3300, 36300], [47887, 540, 5940, 7260], [23867, 5340, 7140, 65340]], 'aut_group': None, 'aut_hash': 285222220836962771, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 25555200, 'aut_permdeg': 268, 'aut_perms': [52082089710798136582338863059328821362200001497628828732322286774141560292110765676991004553988317954654231249971422120741920889281419920481132844259739919262087988056578885862925142585350171656314677380066114168743229929721440451844215356016806250752518541604438031751732366189770584949592208460974771077472837758424995069349845090344022939365897974640147332880418953582390124918839311496823405590167231512264917696469332645825633755516402544102994810515151549852308080031635754101252916798589268113722128381206602327323855284719223234, 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18708336307213486318050860659158729390577577720143026492565604932604592579104918772663380328799056473324788768914565958248712539982234890450557688921498809399733510623075553557727393954758913822014772807944225205606148194436120571172637387298539202000988600003214904065402745750635638706492965618327555264020208006808176856024674427732833321160129416529876382710681523903802475093615354425521734720314285066755258413978498630859629222203092250152767682318510281627896922900227606450725087278381074418855990663656880687983830454987246859, 24709859830903443346659020799533473282814136479882654527194354046544529702383887894902700161176294403255184885674437436483051837497623936893414548538713062590973069644680989622552183961993549533605044260708501384087831741743084515261641469111462520612352825005398226582072531845632906901820122544632642749746893049278941323391490499195615084098302957976994166252301387708166723587919951040593611958465793809276363599615799463941912260613513715266438106783260421906030593820996198973789602891637448613307891692548342217235033619920828342], '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], [5, 1, 4, 1], [6, 121, 2, 1], [10, 1, 4, 1], [11, 2, 5, 1], [11, 3, 40, 1], [11, 6, 200, 1], [12, 1331, 4, 1], [15, 121, 8, 1], [20, 11, 8, 1], [22, 2, 5, 1], [22, 3, 40, 1], [22, 6, 200, 1], [30, 121, 8, 1], [33, 242, 10, 1], [44, 33, 80, 1], [55, 2, 20, 1], [55, 3, 160, 1], [55, 6, 800, 1], [60, 1331, 16, 1], [66, 242, 10, 1], [110, 2, 20, 1], [110, 3, 160, 1], [110, 6, 800, 1], [165, 242, 40, 1], [220, 33, 320, 1], [330, 242, 40, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^3.C_{60}.C_{20}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '8.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_4', '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], [5, 1, 4], [6, 121, 2], [10, 1, 4], [11, 2, 5], [11, 3, 40], [11, 6, 200], [12, 1331, 4], [15, 121, 8], [20, 11, 8], [22, 2, 5], [22, 3, 40], [22, 6, 200], [30, 121, 8], [33, 242, 10], [44, 33, 80], [55, 2, 20], [55, 3, 160], [55, 6, 800], [60, 1331, 16], [66, 242, 10], [110, 2, 20], [110, 3, 160], [110, 6, 800], [165, 242, 40], [220, 33, 320], [330, 242, 40]], 'center_label': '10.2', 'center_order': 10, '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', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['363.2', 1], ['44.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 121, 2, 1], [4, 11, 2, 1], [5, 1, 4, 1], [6, 121, 2, 1], [10, 1, 4, 1], [11, 2, 5, 1], [11, 3, 10, 4], [11, 6, 10, 20], [12, 1331, 4, 1], [15, 121, 8, 1], [20, 11, 8, 1], [22, 2, 5, 1], [22, 3, 10, 4], [22, 6, 10, 20], [30, 121, 8, 1], [33, 242, 10, 1], [44, 33, 20, 4], [55, 2, 20, 1], [55, 3, 40, 4], [55, 6, 40, 20], [60, 1331, 16, 1], [66, 242, 10, 1], [110, 2, 20, 1], [110, 3, 40, 4], [110, 6, 40, 20], [165, 242, 40, 1], [220, 33, 80, 4], [330, 242, 40, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 660, 'exponents_of_order': [3, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[6, 0, 800]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 8306399108432285892, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [6, 11, 11, 11], 'inner_gens': [[1, 5160, 1200, 72600], [2821, 60, 660, 7260], [121, 60, 660, 7260], [14521, 60, 660, 7260]], 'inner_hash': 7345092711346113254, 'inner_nilpotent': False, 'inner_order': 7986, 'inner_split': True, 'inner_tex': 'C_{11}^3:C_6', 'inner_used': [1, 2, 4], 'irrC_degree': 6, 'irrQ_degree': 240, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 60], [2, 150], [3, 800], [6, 2000]], 'label': '79860.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:C60', '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, 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': 30, 'number_characteristic_subgroups': 30, 'number_conjugacy_classes': 3010, 'number_divisions': 124, 'number_normal_subgroups': 30, 'number_subgroup_autclasses': 68, 'number_subgroup_classes': 256, 'number_subgroups': 5312, 'old_label': None, 'order': 79860, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 1], [3, 242], [4, 22], [5, 4], [6, 242], [10, 4], [11, 1330], [12, 5324], [15, 968], [20, 88], [22, 1330], [30, 968], [33, 2420], [44, 2640], [55, 5320], [60, 21296], [66, 2420], [110, 5320], [165, 9680], [220, 10560], [330, 9680]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 40, 'outer_gen_orders': [40, 20, 20, 20, 20], 'outer_gen_pows': [4, 0, 0, 0, 4], 'outer_gens': [[19, 3900, 6420, 72600], [47, 720, 7020, 36300], [17, 7020, 3180, 7260], [29, 3720, 3000, 43560], [37, 6240, 1260, 72600]], 'outer_group': None, 'outer_hash': 2682263260165825920, 'outer_nilpotent': True, 'outer_order': 3200, 'outer_permdeg': 24, 'outer_perms': [28258285232236823372256, 109286086613077788029344, 27139143547792900108864, 129265193148433090398720, 56207700031688212099770], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': '(C_{10}\\times C_{20}).C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 53, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 3], [4, 3], [8, 3], [10, 2], [16, 1], [20, 2], [30, 8], [40, 2], [60, 44], [80, 2], [120, 8], [240, 44]], 'representations': {'PC': {'code': '193110875976391106384373648759059082842353193354220538950013999', 'gens': [1, 5, 6, 7], 'pres': [7, -2, -2, -3, -5, -11, 11, -11, 14, 36, 79, 180604, 47261, 45168, 50405, 127272, 12619, 3557406]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 6527083114460794, 33418192856010432, 8424221742286342, 19063078487671420, 4764541194236758, 17298483428108842]}, 'Perm': {'d': 53, 'gens': [46800, 88568943663931238728313003404740834564090550910417120297225429415720, 46807, 170720489357293401303315916122635690134759858916799599084743041145080, 253082525453715620387537772320570497622524557293195098649973694585080, 335322689385130611665980495173581446655602006690581864385143193424527, 409807403118736856213848875004765820494532047051849849063591797546137]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [60], '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_{60}', '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': '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': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': '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]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, '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': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
