-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1597200.g', 'ambient_counter': 7, 'ambient_order': 1597200, 'ambient_tex': 'C_{11}^2.C_{132}:C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 319440, 'counter': 23, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1597200.g.5._.C', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '5.C', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '5.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 5, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_5', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '319440.x', 'subgroup_hash': None, 'subgroup_order': 319440, 'subgroup_tex': 'C_{11}^3:(C_{10}\\times D_{12})', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1597200.g', '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': [27896588251246387, 23124222817174264, 34951316363147629, 8128620402584133, 9680781872755444, 42949446787370276, 41892009063798686, 6531256166667508, 4075352433795022], 'label': '1597200.g.5._.C', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '5.C', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '5._.C', 'subgroup_fusion': None, 'weyl_group': None}
-
gps_groups • Show schema
Hide schema
{'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}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '200.52', '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': [[19358111333213666, 2933956861135506, 19063078487671420, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [36659785010902224, 14056051161881210, 44332910598934272, 30831531785136107, 31922051514646106, 17021285800720109, 16709096428005216, 29240918749009128, 21237661053449171, 35182165658670510], [3623718842571447, 12028054800124037, 11093250843123849, 40125607717732956, 16184183317962423, 4322230773127066, 16709096428005216, 29240918749009128, 33493281462077598, 32566862292161106], [45070830104294338, 16139266163621954, 11624334538179246, 30712996999230637, 44248504859984487, 33317722748990331, 16709096428005216, 29240918749009128, 2626517522476736, 38481636373612647], [4502960652448201, 45263651578141733, 2177486419203607, 25743711592703251, 17977446687736707, 19612860483268022, 16709096428005216, 29240918749009128, 22900955157734819, 10708869986127018], [6213204634763534, 3095761334794914, 40773554606727922, 19065224337964314, 28416424197994573, 20332402498640353, 37595466963011736, 8354548214002608, 39935675595367894, 22037259056683750], [9857279998094738, 8483677609258266, 26536375970473008, 3297695185508478, 29536998733982169, 12577487983513731, 12531822321003912, 33418192856010432, 867786878173936, 12089249341351951], [35247341951050680, 17840103241826478, 11476818138598258, 5913283844201322, 32304965803407930, 26827201240716362, 12531822321003912, 33418192856010432, 31885808714184975, 29390894580800373]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 255552000, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 660.0, '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], [5, 1331, 5, 4], [6, 242, 1, 1], [6, 2662, 2, 1], [10, 1, 4, 1], [10, 66, 8, 1], [10, 726, 8, 1], [10, 1331, 5, 4], [10, 1331, 8, 1], [10, 1331, 10, 4], [10, 7986, 10, 8], [11, 10, 1, 1], [11, 30, 2, 1], [11, 60, 1, 1], [11, 60, 10, 1], [11, 120, 5, 1], [12, 242, 2, 1], [12, 2662, 2, 1], [15, 242, 4, 1], [15, 2662, 5, 4], [20, 22, 4, 1], [20, 242, 4, 1], [20, 2662, 5, 8], [22, 10, 1, 1], [22, 30, 2, 1], [22, 60, 1, 1], [22, 60, 10, 1], [22, 120, 5, 1], [22, 660, 2, 2], [22, 660, 20, 1], [22, 7260, 2, 1], [30, 242, 4, 1], [30, 2662, 5, 4], [30, 2662, 8, 1], [30, 2662, 10, 4], [33, 2420, 1, 1], [44, 660, 2, 2], [44, 2420, 1, 1], [55, 10, 4, 1], [55, 30, 8, 1], [55, 60, 4, 1], [55, 60, 40, 1], [55, 120, 20, 1], [60, 242, 8, 1], [60, 2662, 8, 1], [60, 2662, 10, 8], [66, 2420, 1, 1], [110, 10, 4, 1], [110, 30, 8, 1], [110, 60, 4, 1], [110, 60, 40, 1], [110, 120, 20, 1], [110, 660, 8, 2], [110, 660, 80, 1], [110, 7260, 8, 1], [132, 2420, 2, 1], [165, 2420, 4, 1], [220, 660, 8, 2], [220, 2420, 4, 1], [330, 2420, 4, 1], [660, 2420, 8, 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], [5, 1331, 20], [6, 242, 1], [6, 2662, 2], [10, 1, 4], [10, 66, 8], [10, 726, 8], [10, 1331, 68], [10, 7986, 80], [11, 10, 1], [11, 30, 2], [11, 60, 11], [11, 120, 5], [12, 242, 2], [12, 2662, 2], [15, 242, 4], [15, 2662, 20], [20, 22, 4], [20, 242, 4], [20, 2662, 40], [22, 10, 1], [22, 30, 2], [22, 60, 11], [22, 120, 5], [22, 660, 24], [22, 7260, 2], [30, 242, 4], [30, 2662, 68], [33, 2420, 1], [44, 660, 4], [44, 2420, 1], [55, 10, 4], [55, 30, 8], [55, 60, 44], [55, 120, 20], [60, 242, 8], [60, 2662, 88], [66, 2420, 1], [110, 10, 4], [110, 30, 8], [110, 60, 44], [110, 120, 20], [110, 660, 96], [110, 7260, 8], [132, 2420, 2], [165, 2420, 4], [220, 660, 16], [220, 2420, 4], [330, 2420, 4], [660, 2420, 8]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, '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', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['319440.e', 1], ['5.1', 1]], '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], [5, 1331, 4, 5], [6, 242, 1, 1], [6, 2662, 1, 2], [10, 1, 4, 1], [10, 66, 4, 2], [10, 726, 4, 2], [10, 1331, 4, 17], [10, 7986, 4, 20], [11, 10, 1, 1], [11, 30, 1, 2], [11, 60, 1, 11], [11, 120, 1, 5], [12, 242, 2, 1], [12, 2662, 2, 1], [15, 242, 4, 1], [15, 2662, 4, 5], [20, 22, 4, 1], [20, 242, 4, 1], [20, 2662, 4, 10], [22, 10, 1, 1], [22, 30, 1, 2], [22, 60, 1, 11], [22, 120, 1, 5], [22, 660, 1, 24], [22, 7260, 1, 2], [30, 242, 4, 1], [30, 2662, 4, 17], [33, 2420, 1, 1], [44, 660, 1, 2], [44, 660, 2, 1], [44, 2420, 1, 1], [55, 10, 4, 1], [55, 30, 4, 2], [55, 60, 4, 11], [55, 120, 4, 5], [60, 242, 8, 1], [60, 2662, 8, 11], [66, 2420, 1, 1], [110, 10, 4, 1], [110, 30, 4, 2], [110, 60, 4, 11], [110, 120, 4, 5], [110, 660, 4, 24], [110, 7260, 4, 2], [132, 2420, 2, 1], [165, 2420, 4, 1], [220, 660, 4, 2], [220, 660, 8, 1], [220, 2420, 4, 1], [330, 2420, 4, 1], [660, 2420, 8, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 660, 'exponents_of_order': [4, 3, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[60, 0, 80], [120, 0, 20]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 2259044285002751269, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [10, 10, 11, 11, 5, 10, 1, 1, 30, 11], 'inner_gens': [[19358111333213666, 3578721171773324, 17239527064479801, 42568624234005174, 8266640929675533, 13670621100413654, 12531822321003912, 33418192856010432, 11516284109019977, 30035389480921159], [26416454896672115, 2933956861135506, 44714044401394707, 942272443149000, 44276413698111540, 24315254825686434, 12531822321003912, 33418192856010432, 45933676238210354, 9889029950877890], [18181120304346870, 20463331180269941, 19063078487671420, 17298483428108842, 6443374818154525, 38258784811600803, 12531822321003912, 33418192856010432, 37960645460909649, 4764541194236758], [44631079532766360, 20581598879797571, 19063078487671420, 17298483428108842, 41922377452032715, 18755875514225348, 12531822321003912, 33418192856010432, 9693813549698132, 4764541194236758], [17154781781066514, 12609920733236825, 20123654429140706, 27238780040815509, 5912944201328162, 13140307079051117, 12531822321003912, 33418192856010432, 34167653853121506, 14708290010338879], [25921905219956196, 17370708274012920, 42891146272563895, 45451992243043449, 43745275600511749, 10522401710269773, 12531822321003912, 33418192856010432, 26375648796824317, 26126965308031858], [19358111333213666, 2933956861135506, 19063078487671420, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [19358111333213666, 2933956861135506, 19063078487671420, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758], [15681347858950854, 24373688374438059, 1531656888644363, 8269385602214435, 6445834230877611, 37678271249731280, 12531822321003912, 33418192856010432, 20283505689400384, 25596195191350702], [9417475222423888, 12608275112311139, 19063078487671420, 17298483428108842, 41127567222052213, 12344066370653464, 12531822321003912, 33418192856010432, 44754555010279833, 4764541194236758]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 159720, 'inner_split': None, 'inner_tex': None, 'inner_used': None, 'irrC_degree': 60, 'irrQ_degree': 240, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 200], [2, 250], [10, 20], [20, 25], [30, 40], [60, 230], [120, 50]], 'label': '1597200.g', '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': 'C11^2.C132:C10^2', 'ngens': 10, '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, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 3, 0, 1, 0, 0, 1, 0, 3, 1, 0, 0, 1, 1, 0, 0, 3, 0, 0, 0, 6, 3, 3, 0, 0, 1, 0, 0, 18, 1, 7, 0, 6, 0, 0, 18, 0, 7, 1, 0, 18, 0, 6, 1, 3, 0, 42, 1, 0, 3, 0, 42, 3, 1, 6, 7, 0, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 112, 'number_characteristic_subgroups': 69, 'number_conjugacy_classes': 815, 'number_divisions': 254, 'number_normal_subgroups': 244, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1597200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 4247], [3, 242], [4, 264], [5, 26624], [6, 5566], [10, 735728], [11, 1330], [12, 5808], [15, 54208], [20, 107536], [22, 31690], [30, 181984], [33, 2420], [44, 5060], [55, 5320], [60, 236192], [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': '1600.10076', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 1600, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'D_4\\times C_{10}\\times F_5', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 53, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 6], [4, 50], [8, 36], [10, 4], [16, 12], [20, 3], [30, 8], [40, 5], [60, 44], [80, 3], [120, 19], [160, 1], [240, 44], [480, 11]], 'representations': {'PC': {'code': '57379087005666680432353780236896489498131045818451143136730012772945170709904437842802807930611360891416157350223821724967256160837054637703917917760281850051873604215853731371524564059039037073401129308193627161222290301003999', 'gens': [1, 3, 5, 9, 10], 'pres': [10, -2, -5, -2, -3, -2, -2, -5, -11, 11, 11, 20, 17641502, 4518162, 82, 34849603, 3000413, 29133004, 121514, 1488324, 729184, 144, 69919205, 291615, 3492745, 1749995, 175, 51340806, 218416, 8149706, 4083276, 416, 35712007, 192017, 8131227, 4113637, 2376008, 2376018, 1188028, 198048, 29040009, 29040019, 1488029, 18039]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [19358111333213666, 2933956861135506, 19063078487671420, 17298483428108842, 5912944201328162, 10522401710269773, 12531822321003912, 33418192856010432, 20283505689400384, 4764541194236758]}, 'Perm': {'d': 53, 'gens': [34, 88693108456544472778195665707039717461646397097730576937158031532871, 164722742746385302442147457927510235995094770080576706805649173850953, 253107450449214080387248509700077510740070409702103700025524414250871, 90754, 335383062439046829904667434356584809345232451589925760737168321337634, 88693145698290584412723081234098777828537839220917766063181530880073, 406642088921882847167578008062422250166609515202567918073748809665120, 497911751831218128246779007287258932031686567015037018141853484890835, 567772305046272712597006046357249548267035647000964195159599006054473]}}, 'schur_multiplier': [2, 2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 300, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_{11}^2.C_{132}:C_{10}^2', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '5.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [2]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', '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': 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], [5, 1, 4]], 'center_label': '5.1', 'center_order': 5, 'central_product': False, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['5.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [5, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 5, 'eulerian_function': 1, 'exponent': 5, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '5.1', 'hash': 1, 'hyperelementary': 5, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1], 'inner_gens': [[1]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': 1, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 5]], 'label': '5.1', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C5', 'ngens': 1, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 5, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 5, 'order_factorization_type': 1, 'order_stats': [[1, 1], [5, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 5, 'pgroup': 5, 'primary_abelian_invariants': [5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -5]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [26329372]}, 'Lie': [{'d': 1, 'q': 5, 'gens': [33], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 5, 'gens': [131]}, 'Perm': {'d': 5, 'gens': [96]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [5], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_5', 'transitive_degree': 5, 'wreath_data': None, 'wreath_product': False}
