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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '32440320.b', 'ambient_counter': 2, 'ambient_order': 32440320, 'ambient_tex': 'C_2^{12}.M_{11}', 'central': False, 'central_factor': False, 'centralizer_order': 4096, 'characteristic': True, 'core_order': 2048, 'counter': 771, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '32440320.b.15840.A', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '15840.a1.N', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '15840.q', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8034936889538388295, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 15840, 'quotient_simple': False, 'quotient_solvable': False, 'quotient_supersolvable': False, 'quotient_tex': 'C_2\\times M_{11}', 'simple': False, 'solvable': True, 'special_labels': ['S', 'C2'], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': None, 'subgroup_hash': 595564629897153398, 'subgroup_order': 2048, 'subgroup_tex': 'C_2^{11}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '32440320.b', 'aut_centralizer_order': None, 'aut_label': '15840.A', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '7920.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '15840.A', 'coset_action_label': None, 'count': 1, 'diagramx': [-1, 5364, -1, 7594], 'generators': [10904380660461683146792284847, 5167, 20411645834288669703686597719606480360978601647, 60448715589986999452694982546765003886292141083473967, 122000787836928007, 1313901393960, 8231691320578226211045097771008000, 5160, 25903229683158464676480, 10341831284004956816162169531924520279680, 40279687], 'label': '32440320.b.15840.A', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '15840.A', 'normal_contained_in': [], 'normal_contains': [], 'normalizer': '1.a1', 'old_label': '15840.a1.N', 'projective_image': '16220160.c', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '15840.A', 'subgroup_fusion': None, 'weyl_group': '7920.a'}
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label None does not appear in gps_groups
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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': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 2640, 'aut_gen_orders': [12, 8], 'aut_gens': [[2597822231175200806981867153230934918340651343615134662, 1173762232736947426780548442374037783095951697921680006], [247418359828361213119399699278523748650516592958820433, 184056533586655546047944070050207743194704488405564782], [2474181860279783736039028682899760284468905544084087102, 926343851408647768941575504966544570458206768111699206]], 'aut_group': '32440320.b', 'aut_hash': 7803173533006989596, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 32440320, 'aut_permdeg': 2664, 'aut_perms': 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'aut_phi_ratio': 4.125, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [2, 12, 2, 1], [2, 55, 1, 2], [2, 66, 1, 2], [2, 132, 2, 1], [2, 165, 1, 2], [2, 220, 2, 1], [2, 330, 1, 2], [2, 396, 1, 2], [2, 660, 2, 1], [2, 2640, 1, 2], [2, 7920, 1, 2], [2, 10560, 2, 1], [3, 28160, 1, 1], [4, 2640, 1, 2], [4, 7920, 1, 2], [4, 10560, 1, 4], [4, 10560, 2, 3], [4, 15840, 1, 4], [4, 31680, 1, 6], [4, 31680, 2, 4], [4, 126720, 1, 4], [4, 253440, 2, 1], [5, 405504, 1, 1], [6, 28160, 1, 3], [6, 28160, 2, 2], [6, 56320, 1, 2], [6, 56320, 2, 1], [6, 84480, 1, 4], [6, 84480, 2, 2], [6, 168960, 1, 2], [6, 168960, 2, 1], [6, 337920, 1, 2], [6, 337920, 2, 1], [8, 126720, 1, 4], [8, 253440, 1, 4], [8, 253440, 2, 3], [8, 506880, 1, 4], [8, 506880, 2, 2], [10, 405504, 1, 7], [10, 405504, 2, 4], [11, 737280, 1, 2], [12, 337920, 1, 6], [12, 337920, 2, 3], [16, 506880, 1, 4], [16, 506880, 2, 2], [22, 737280, 1, 2], [22, 737280, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^{12}.M_{11}', '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': 2640, 'autcentquo_group': '16220160.c', 'autcentquo_hash': 7358568238328148264, 'autcentquo_nilpotent': False, 'autcentquo_order': 16220160, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^{11}.M_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [2, 12, 2], [2, 55, 2], [2, 66, 2], [2, 132, 2], [2, 165, 2], [2, 220, 2], [2, 330, 2], [2, 396, 2], [2, 660, 2], [2, 2640, 2], [2, 7920, 2], [2, 10560, 2], [3, 28160, 1], [4, 2640, 2], [4, 7920, 2], [4, 10560, 10], [4, 15840, 4], [4, 31680, 14], [4, 126720, 4], [4, 253440, 2], [5, 405504, 1], [6, 28160, 7], [6, 56320, 4], [6, 84480, 8], [6, 168960, 4], [6, 337920, 4], [8, 126720, 4], [8, 253440, 10], [8, 506880, 8], [10, 405504, 15], [11, 737280, 2], [12, 337920, 12], [16, 506880, 8], [22, 737280, 6]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '16220160.c', 'commutator_count': 1, 'commutator_label': '8110080.a', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '7920.a'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['16220160.c', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [2, 12, 1, 2], [2, 55, 1, 2], [2, 66, 1, 2], [2, 132, 1, 2], [2, 165, 1, 2], [2, 220, 1, 2], [2, 330, 1, 2], [2, 396, 1, 2], [2, 660, 1, 2], [2, 2640, 1, 2], [2, 7920, 1, 2], [2, 10560, 1, 2], [3, 28160, 1, 1], [4, 2640, 1, 2], [4, 7920, 1, 2], [4, 10560, 1, 10], [4, 15840, 1, 4], [4, 31680, 1, 14], [4, 126720, 1, 4], [4, 253440, 1, 2], [5, 405504, 1, 1], [6, 28160, 1, 7], [6, 56320, 1, 4], [6, 84480, 1, 8], [6, 168960, 1, 4], [6, 337920, 1, 4], [8, 126720, 1, 4], [8, 253440, 1, 10], [8, 506880, 2, 4], [10, 405504, 1, 7], [10, 405504, 2, 4], [11, 737280, 2, 1], [12, 337920, 1, 12], [16, 506880, 2, 4], [22, 737280, 2, 3]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 2640, 'exponents_of_order': [16, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[22, 1, 1], [66, 1, 4], [110, 1, 6], [165, 1, 4], [176, 1, 2], [198, 1, 1], [220, 1, 2], [264, 1, 4], [330, 0, 4], [330, 1, 10], [396, 1, 2], [440, 1, 4], [495, 1, 4], [660, 1, 4], [792, 1, 2], [990, 1, 4], [1584, 1, 2]], 'familial': False, 'frattini_label': '1024.djt', 'frattini_quotient': '31680.l', 'hash': 7803173533006989596, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 2640, 'inner_gen_orders': [12, 8], 'inner_gens': [[2597822231175200806981867153230934918340651343615134662, 1237090898440422159293978598175617141217292033948337337], [1792376355229743524169383722272148745030839472302610040, 1173762232736947426780548442374037783095951697921680006]], 'inner_hash': 7358568238328148264, 'inner_nilpotent': False, 'inner_order': 16220160, 'inner_split': True, 'inner_tex': 'C_2^{11}.M_{11}', 'inner_used': [1, 2], 'irrC_degree': 22, 'irrQ_degree': 22, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 4], [10, 12], [11, 4], [16, 8], [22, 2], [44, 4], [45, 4], [55, 4], [66, 8], [110, 12], [165, 8], [176, 4], [198, 2], [220, 4], [264, 8], [330, 28], [396, 4], [440, 8], [495, 8], [660, 8], [792, 4], [990, 8], [1584, 4]], 'label': '32440320.b', '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': False, 'name': 'C2^12.M11', 'ngens': 2, '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, 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, 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, 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, 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': 124, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 160, 'number_divisions': 144, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 32440320, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 46335], [3, 28160], [4, 1647360], [5, 405504], [6, 3125760], [8, 7096320], [10, 6082560], [11, 1474560], [12, 4055040], [16, 4055040], [22, 4423680]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2658270926353531630298162738952571852502574817130148617, 1113313537531068430985867394269909454530305990192739881]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 44, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [10, 4], [11, 4], [20, 4], [22, 2], [32, 4], [44, 4], [45, 4], [55, 4], [66, 8], [110, 12], [165, 8], [198, 2], [220, 4], [264, 8], [330, 20], [352, 2], [396, 4], [440, 8], [495, 8], [660, 12], [792, 4], [990, 8], [3168, 2]], 'representations': {'Perm': {'d': 44, 'gens': [1173762232736947426780548442374037783095951697921680006, 2597822231175200806981867153230934918340651343615134662]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 1584, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^{12}.M_{11}', 'transitive_degree': 44, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 1320, 'aut_gen_orders': [11, 5, 4], 'aut_gens': [[487127904, 1046351545], [340072008, 4112779255], [261497160, 2737270831], [1522120728, 4451102689]], 'aut_group': '7920.a', 'aut_hash': 3986485404724135366, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7920, 'aut_permdeg': 165, 'aut_perms': [47907267265481101173971549131888055024170340835276204336620451611739360841579006112653262080552815204272619187295379055451158685508512858668699319091564993972770582068119488084100172746282288487961469192940998529314010267016800647142452742566187967368099082404696019935100129094498029468492873627, 48158751562725333351363769146438536282587738777483267801417619937264176889077831424375438477704235650918907367418575536960185709123835668006147095304827012640919166207187393411462519491268281239514017559803859625458531921114524159698583306919194175304195821142288771979200604681416988347185789895, 42260074587349889336386068922998332105058046044980170769717583796681836057761873331767813969192665436114016968793016683371430918116917685520291904376257469210570026627100743268344407053657177692528716523498845640016550904045831050849674263296458388165412655609328422544323403831852435139424199380], 'aut_phi_ratio': 2.0625, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 165, 1, 2], [3, 440, 1, 1], [4, 990, 1, 2], [5, 1584, 1, 1], [6, 440, 1, 1], [6, 1320, 1, 2], [8, 990, 1, 4], [10, 1584, 1, 1], [11, 720, 1, 2], [22, 720, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'M_{11}', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '7920.a', 'autcentquo_hash': 3986485404724135366, 'autcentquo_nilpotent': False, 'autcentquo_order': 7920, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'M_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 165, 2], [3, 440, 1], [4, 990, 2], [5, 1584, 1], [6, 440, 1], [6, 1320, 2], [8, 990, 4], [10, 1584, 1], [11, 720, 2], [22, 720, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '7920.a', 'commutator_count': 1, 'commutator_label': '7920.a', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '7920.a'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['7920.a', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 165, 1, 2], [3, 440, 1, 1], [4, 990, 1, 2], [5, 1584, 1, 1], [6, 440, 1, 1], [6, 1320, 1, 2], [8, 990, 2, 2], [10, 1584, 1, 1], [11, 720, 2, 1], [22, 720, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 19434, 'exponent': 1320, 'exponents_of_order': [5, 2, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[10, 0, 2], [10, 1, 1], [11, 1, 1], [16, 0, 2], [44, 1, 1], [45, 1, 1], [55, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '15840.q', 'hash': 8034936889538388295, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 1320, 'inner_gen_orders': [8, 5], 'inner_gens': [[487127904, 2582840449], [5001424686, 1046351545]], 'inner_hash': 3986485404724135366, 'inner_nilpotent': False, 'inner_order': 7920, 'inner_split': True, 'inner_tex': 'M_{11}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 10, 'irrQ_dim': 10, 'irrR_degree': 10, 'irrep_stats': [[1, 2], [10, 6], [11, 2], [16, 4], [44, 2], [45, 2], [55, 2]], 'label': '15840.q', 'linC_count': 3, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 1, 'linQ_dim': 10, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'C2*M11', 'ngens': 2, '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, 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': 20, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 16, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 114, 'number_subgroup_classes': 114, 'number_subgroups': 29116, 'old_label': None, 'order': 15840, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 331], [3, 440], [4, 1980], [5, 1584], [6, 3080], [8, 3960], [10, 1584], [11, 1440], [22, 1440]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': None, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [10, 2], [11, 2], [20, 2], [32, 2], [44, 2], [45, 2], [55, 2]], 'representations': {'Perm': {'d': 13, 'gens': [487127904, 1046351545]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times M_{11}', 'transitive_degree': 22, 'wreath_data': None, 'wreath_product': False}
