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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1584.135', 'ambient_counter': 135, 'ambient_order': 1584, 'ambient_tex': 'D_{44}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 2, 'counter': 116, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1584.135.792.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '792.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 42, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 792, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{18}\\times D_{22}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1584.135', 'aut_centralizer_order': 10560, 'aut_label': '792.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 10560, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['72.a1.a1', '264.a1.a1', '396.a1.a1', '396.b1.a1', '396.c1.a1', '396.d1.a1', '396.d1.b1', '396.e1.a1', '396.e1.b1'], 'contains': ['1584.a1.a1'], 'core': '792.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6348, 5356, 7178, 6109, 7082, 5653, 7014, 6906], 'generators': [24778026504], 'label': '1584.135.792.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '792.a1.a1', 'normal_contained_in': ['72.a1.a1', '264.a1.a1', '396.a1.a1', '396.b1.a1', '396.c1.a1'], 'normal_contains': ['1584.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '792.a1.a1', 'projective_image': '792.42', 'quotient_action_image': '1.1', 'quotient_action_kernel': '792.42', 'quotient_action_kernel_order': 792, 'quotient_fusion': None, 'short_label': '792.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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, 1]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], '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': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': '72.18', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [30, 30, 30, 10, 30, 30], 'aut_gens': [[20085218158, 15767835078, 158006], [8071630041, 13390145691, 39829422], [19084085794, 125141745, 2630125], [11137597909, 24715455533, 52496104], [22212624680, 22838332207, 42481779], [10824743978, 16831538151, 19925033], [1439128060, 500566333, 19694773]], 'aut_group': None, 'aut_hash': 569556090490505273, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10560, 'aut_permdeg': 52, 'aut_perms': [48321365600027051791705374226123915231552038434527987942974801234328, 53529491512083415265386096238883155640531079342338147044980537600, 41602690302509284389960037993933877387991798471346123225459346867786, 43594822256310757593559926513812906605673710575960074655020038322758, 26186394043978570311966781269705826796530566250827259238131247334637, 12752130449931557312787887936856259303113686997176769413755472523513], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 2, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 22, 2, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 22, 4, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 22, 4, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 22, 12, 1], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 22, 12, 1], [44, 2, 10, 2], [66, 2, 10, 1], [66, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.C_{30}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '220.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 220, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 22, 2], [3, 1, 2], [4, 1, 2], [4, 2, 1], [4, 22, 2], [6, 1, 2], [6, 2, 2], [6, 22, 4], [9, 1, 6], [11, 2, 5], [12, 1, 4], [12, 2, 2], [12, 22, 4], [18, 1, 6], [18, 2, 6], [18, 22, 12], [22, 2, 15], [33, 2, 10], [36, 1, 12], [36, 2, 6], [36, 22, 12], [44, 2, 20], [66, 2, 30], [99, 2, 30], [132, 2, 40], [198, 2, 90], [396, 2, 120]], 'center_label': '36.2', 'center_order': 36, 'central_product': True, 'central_quotient': '44.3', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 135, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['176.30', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 1, 2], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 22, 1, 2], [6, 1, 2, 1], [6, 2, 2, 1], [6, 22, 2, 2], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 22, 2, 2], [18, 1, 6, 1], [18, 2, 6, 1], [18, 22, 6, 2], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 22, 6, 2], [44, 2, 10, 2], [66, 2, 10, 1], [66, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 117936, 'exponent': 396, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 120]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '264.36', 'hash': 135, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [22, 22, 2], 'inner_gens': [[20085218158, 15767835078, 60098257], [20085218158, 15767835078, 19694773], [1564269646, 17644958238, 158006]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 44, 'inner_split': True, 'inner_tex': 'D_{22}', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': 4, 'irrep_stats': [[1, 72], [2, 378]], 'label': '1584.135', 'linC_count': 120, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 32, 'linQ_dim': 20, 'linQ_dim_count': 32, 'linR_count': 60, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D44:C18', 'ngens': 3, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 45, 'number_conjugacy_classes': 450, 'number_divisions': 42, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 120, 'number_subgroups': 588, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 48], [6, 94], [9, 6], [11, 10], [12, 96], [18, 282], [22, 30], [33, 20], [36, 288], [44, 40], [66, 60], [99, 60], [132, 80], [198, 180], [396, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 19522081261], 'outer_gens': [[23276327632, 7195639040, 158006], [23276327632, 17644958238, 158006], [7946488521, 15767835078, 158006], [23401469218, 24340030945, 52666417]], 'outer_group': '240.208', 'outer_hash': 208, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [40279680, 1307674368000, 362880, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 1], [6, 8], [8, 1], [10, 4], [20, 4], [24, 1], [40, 1], [60, 4], [80, 1], [240, 1]], 'representations': {'PC': {'code': 302294354905805879501193278953540000119, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, 2, -3, -3, -11, 36, 24531, 80, 5604, 137, 20165, 166, 70566]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [20085218158, 15767835078, 158006]}, 'Perm': {'d': 28, 'gens': [10921132818399422783324528047, 23020551001543316243742720000, 1629375110092645594398720000, 135184941877708800, 34341896591985019623505920000, 263631088065945600, 4364893]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 18], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{44}:C_{18}', 'transitive_degree': 792, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '72.18', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [30, 30, 10, 30], 'aut_gens': [[1, 2, 4], [1, 686, 764], [396, 687, 345], [396, 434, 537], [397, 254, 689]], 'aut_group': None, 'aut_hash': 6081326650477710845, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 15840, 'aut_permdeg': 50, 'aut_perms': [6678429564033365973809682866454074944975752707853442376348928000, 2062585570836601159028557233503552345123063339236213189466268230, 14258779078444865233199555526324429017565706269782178523758856152, 148461210868060168483337233748040088781736255315184540046589357], 'aut_phi_ratio': 66.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 11, 4, 1], [3, 1, 2, 1], [6, 1, 6, 1], [6, 11, 8, 1], [9, 1, 6, 1], [11, 2, 5, 1], [18, 1, 18, 1], [18, 11, 24, 1], [22, 2, 15, 1], [33, 2, 10, 1], [66, 2, 30, 1], [99, 2, 30, 1], [198, 2, 90, 1]], 'aut_supersolvable': False, 'aut_tex': '(C_{11}\\times A_4).C_{30}.C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '144.188', 'autcent_hash': 188, 'autcent_nilpotent': False, 'autcent_order': 144, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_6\\times S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 11, 4], [3, 1, 2], [6, 1, 6], [6, 11, 8], [9, 1, 6], [11, 2, 5], [18, 1, 18], [18, 11, 24], [22, 2, 15], [33, 2, 10], [66, 2, 30], [99, 2, 30], [198, 2, 90]], 'center_label': '36.5', 'center_order': 36, 'central_product': True, 'central_quotient': '22.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 42, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['22.1', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 11, 1, 4], [3, 1, 2, 1], [6, 1, 2, 3], [6, 11, 2, 4], [9, 1, 6, 1], [11, 2, 5, 1], [18, 1, 6, 3], [18, 11, 6, 4], [22, 2, 5, 3], [33, 2, 10, 1], [66, 2, 10, 3], [99, 2, 30, 1], [198, 2, 30, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 9828, 'exponent': 198, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '264.36', 'hash': 42, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [1, 2, 11], 'inner_gens': [[1, 2, 4], [1, 2, 436], [1, 362, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 22, 'inner_split': True, 'inner_tex': 'D_{11}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 72], [2, 180]], 'label': '792.42', 'linC_count': 4320, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 16, 'linQ_degree_count': 12, 'linQ_dim': 16, 'linQ_dim_count': 12, 'linR_count': 180, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C18*D22', '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': 252, 'number_divisions': 36, 'number_normal_subgroups': 63, 'number_subgroup_autclasses': 36, 'number_subgroup_classes': 96, 'number_subgroups': 426, 'old_label': None, 'order': 792, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 47], [3, 2], [6, 94], [9, 6], [11, 10], [18, 282], [22, 30], [33, 20], [66, 60], [99, 60], [198, 180]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [2, 6, 6, 10], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[397, 398, 436], [396, 399, 357], [1, 3, 700], [1, 398, 580]], 'outer_group': '720.814', 'outer_hash': 814, 'outer_nilpotent': False, 'outer_order': 720, 'outer_permdeg': 14, 'outer_perms': [1, 3628803, 6706022423, 136087], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'S_4\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [6, 8], [10, 4], [20, 4], [60, 4]], 'representations': {'PC': {'code': 2330109524848259235855388000119, 'gens': [1, 2, 3], 'pres': [6, -2, -2, -2, -3, -3, -11, 3932, 50, 969, 93, 3610, 118, 12971]}, 'GLZN': {'d': 2, 'p': 99, 'gens': [9703000, 86361164, 86356700, 973567, 1622644, 971191]}, 'Perm': {'d': 24, 'gens': [87657660847, 87657292800, 186810624000, 28204889452350234624000, 55236972840318517248000, 4364893]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 18], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{18}\\times D_{22}', 'transitive_degree': 396, 'wreath_data': None, 'wreath_product': False}
