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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4400.q', 'ambient_counter': 17, 'ambient_order': 4400, 'ambient_tex': 'C_{44}:C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 220, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4400.q.20.d1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '20.d1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '20.5', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 5, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 20, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '220.7', 'subgroup_hash': 7, 'subgroup_order': 220, 'subgroup_tex': 'C_2\\times F_{11}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4400.q', 'aut_centralizer_order': 32, 'aut_label': '20.d1', 'aut_quo_index': 3, 'aut_stab_index': 20, 'aut_weyl_group': '220.7', 'aut_weyl_index': 640, 'centralizer': '220.a1', 'complements': ['220.d1', '220.c1'], 'conjugacy_class_count': 20, 'contained_in': ['4.b1', '10.b1', '10.f1'], 'contains': ['40.d1', '40.f1', '100.b1', '220.g1'], 'core': '20.d1', 'coset_action_label': None, 'count': 20, 'diagramx': [4001, 3160, 2395, 3621], 'generators': [50, 22, 400, 2200], 'label': '4400.q.20.d1', 'mobius_quo': 0, 'mobius_sub': -2, 'normal_closure': '20.d1', 'normal_contained_in': ['4.b1', '10.b1', '10.f1'], 'normal_contains': ['40.d1', '100.b1'], 'normalizer': '1.a1', 'old_label': '20.d1', 'projective_image': '2200.a', 'quotient_action_image': '10.2', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '20.d1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 110, 'aut_gen_orders': [10, 22], 'aut_gens': [[1, 10], [1, 130], [11, 10]], 'aut_group': '220.7', 'aut_hash': 7, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 220, 'aut_permdeg': 13, 'aut_perms': [143842590, 982342849], 'aut_phi_ratio': 2.75, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [5, 11, 1, 4], [10, 11, 1, 4], [10, 11, 2, 4], [11, 10, 1, 1], [22, 10, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times F_{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': 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, 1], [2, 11, 2], [5, 11, 4], [10, 11, 12], [11, 10, 1], [22, 10, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '110.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['110.1', 1], ['2.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [5, 11, 4, 1], [10, 11, 4, 3], [11, 10, 1, 1], [22, 10, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 110, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '220.7', 'hash': 7, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11], 'inner_gens': [[1, 130], [101, 10]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 110, 'inner_split': True, 'inner_tex': 'F_{11}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 10, 'irrQ_dim': 10, 'irrR_degree': 10, 'irrep_stats': [[1, 20], [10, 2]], 'label': '220.7', 'linC_count': 1, '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': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*F11', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 17, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 22, 'number_divisions': 10, 'number_normal_subgroups': 12, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 20, 'number_subgroups': 100, 'old_label': None, 'order': 220, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 23], [5, 44], [10, 132], [11, 10], [22, 10]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[111, 210]], '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': 2, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4], [10, 2]], 'representations': {'PC': {'code': 7999992108249490309, 'gens': [1, 3], 'pres': [4, -2, -5, -2, -11, 8, 1562, 906, 34, 643, 647]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [1343, 13320, 9322]}, 'Perm': {'d': 13, 'gens': [40285008, 1, 87910086, 598890408]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times F_{11}', 'transitive_degree': 22, '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': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [20, 20, 4, 2, 20, 20], 'aut_gens': [[1, 10, 100], [2201, 2312, 500], [2207, 1410, 3900], [2203, 1518, 2105], [2209, 1816, 2100], [2203, 2117, 3100], [9, 4117, 500]], 'aut_group': None, 'aut_hash': 4556555602398024433, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 140800, 'aut_permdeg': 143, 'aut_perms': [12015751494156987555228925170674841645285555612291729579892723173022219690491084970898005697873641988273022318634035353356017295878330386042649153558633678410669636204803784611604498640942485272343137965691663038661016137892324917817275130460238874, 34234043115761097408650625404044300178817648649207541662666950452908523371633518098799372841736058945870514981898616269139981295658105720232603382576928698168432743540456440976401080062257928776488254532278547035457155983355571391510524372873659051, 8512535885989870061115561989373365960047924591236996131176497854544087537268841500176830451950734942487995813059023539814467429235124168236925254922019548728703867408994996692964425350056424602562257562173282335468787494473488638386995413742061495, 27003507023037487978963349309051487164952841595684586651043782463415420275280056766747720748511757779992548599713104739714142487338656283515960073099165561817357779911116206414867017882325554321112175980025794930699768631352349028844115897948467415, 4728971208827476279992173687378745848140006803372570465648510965062635224894433003646380690921220144432035142857955551726579750956266031997924729084411365106769252299588791419709217367671939992206422661422833437325762752782244758122029929805441301, 4650049406057583608219906061847526750652541303361457662243508896951314410411785574691464475614829329265579972784429455127314798544820879422547901716007147150417922486906200586564595936362497308608083681437393409827404637775978732892149652157406858], 'aut_phi_ratio': 88.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 22, 4, 1], [4, 2, 2, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 4, 1], [10, 1, 8, 1], [10, 11, 5, 4], [10, 11, 10, 4], [10, 22, 16, 1], [10, 22, 20, 4], [11, 10, 1, 1], [20, 2, 8, 1], [20, 22, 10, 4], [22, 10, 1, 1], [22, 10, 2, 1], [44, 10, 4, 1], [55, 10, 4, 1], [110, 10, 4, 1], [110, 10, 8, 1], [220, 10, 16, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{55}.(C_2^4\\times C_{20}).C_2^3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '640.19303', 'autcent_hash': 19303, 'autcent_nilpotent': False, 'autcent_order': 640, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2\\times F_5', '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, 3], [2, 22, 4], [4, 2, 2], [5, 1, 4], [5, 11, 20], [10, 1, 12], [10, 11, 60], [10, 22, 96], [11, 10, 1], [20, 2, 8], [20, 22, 40], [22, 10, 3], [44, 10, 4], [55, 10, 4], [110, 10, 12], [220, 10, 16]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '220.7', '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', '5.1', '5.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 17, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['440.9', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 22, 1, 4], [4, 2, 1, 2], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 3], [10, 11, 4, 15], [10, 22, 4, 24], [11, 10, 1, 1], [20, 2, 4, 2], [20, 22, 4, 10], [22, 10, 1, 3], [44, 10, 2, 2], [55, 10, 4, 1], [110, 10, 4, 3], [220, 10, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 187488, 'exponent': 220, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2200.a', 'hash': 7612526101672382494, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [1, 10, 22], 'inner_gens': [[1, 10, 100], [1, 10, 3900], [1, 610, 100]], 'inner_hash': 7, 'inner_nilpotent': False, 'inner_order': 220, 'inner_split': False, 'inner_tex': 'C_2\\times F_{11}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 200], [2, 50], [10, 40]], 'label': '4400.q', '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': 'C44:C10^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 38, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 290, 'number_divisions': 82, 'number_normal_subgroups': 168, 'number_subgroup_autclasses': 96, 'number_subgroup_classes': 432, 'number_subgroups': 3200, 'old_label': None, 'order': 4400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 91], [4, 4], [5, 224], [10, 2784], [11, 10], [20, 896], [22, 30], [44, 40], [55, 40], [110, 120], [220, 160]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 2, 4, 4, 10], 'outer_gen_pows': [3300, 0, 0, 0, 0], 'outer_gens': [[1, 3310, 100], [2201, 10, 2100], [3, 18, 2100], [2201, 10, 105], [1, 2211, 100]], 'outer_group': '640.19303', 'outer_hash': 19303, 'outer_nilpotent': False, 'outer_order': 640, 'outer_permdeg': 13, 'outer_perms': [11652480, 3669120, 79, 1041596640, 3612239396], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\wr C_2\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 48], [8, 12], [10, 4], [20, 2], [40, 4], [80, 2]], 'representations': {'PC': {'code': '1659446987753833766528716812695289313362450303009', 'gens': [1, 3, 5], 'pres': [7, -2, -5, -2, -5, -2, -2, -11, 14, 58, 13668, 4400, 102, 14299, 1286, 124, 11780, 2967]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 37668179739389305, 42497879883498899, 33418192856010432, 26794159036998355, 36687300164533435, 17156201816241749]}, 'Perm': {'d': 22, 'gens': [56213599674603571241, 68, 58999653623681971268, 3669908, 10360195344788890361, 110236175353650085241, 12428870892684744960]}}, 'schur_multiplier': [2, 2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{44}:C_{10}^2', 'transitive_degree': 440, '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': '20.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [2, 12], 'aut_gens': [[1, 2], [10, 13], [10, 15]], 'aut_group': '24.5', 'aut_hash': 5, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24, 'aut_permdeg': 7, 'aut_perms': [127, 857], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [5, 1, 4, 1], [10, 1, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4\\times S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '24.5', 'autcent_hash': 5, 'autcent_nilpotent': False, 'autcent_order': 24, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4\\times S_3', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 1, 'autcentquo_group': '1.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 1, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_1', 'cc_stats': [[1, 1, 1], [2, 1, 3], [5, 1, 4], [10, 1, 12]], 'center_label': '20.5', 'center_order': 20, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [5, 1, 4, 1], [10, 1, 4, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 6, 'exponent': 10, 'exponents_of_order': [2, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '20.5', 'hash': 5, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], 'inner_hash': 1, 'inner_nilpotent': True, 'inner_order': 1, 'inner_split': True, 'inner_tex': 'C_1', 'inner_used': [], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 20]], 'label': '20.5', 'linC_count': 72, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 5, 'linQ_degree_count': 6, 'linQ_dim': 5, 'linQ_dim_count': 6, 'linR_count': 12, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C10', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 20, 'number_divisions': 8, 'number_normal_subgroups': 10, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 10, 'number_subgroups': 10, 'old_label': None, 'order': 20, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 3], [5, 4], [10, 12]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 12], 'outer_gen_pows': [0, 0], 'outer_gens': [[10, 13], [10, 15]], 'outer_group': '24.5', 'outer_hash': 5, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [127, 857], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4\\times S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 4]], 'representations': {'PC': {'code': 2179, 'gens': [1, 2], 'pres': [3, -2, -2, -5, 16]}, 'GLZ': {'b': 3, 'd': 5, 'gens': [141602720900, 706303489327]}, 'GLFp': {'d': 2, 'p': 11, 'gens': [13320, 4001]}, 'Perm': {'d': 9, 'gens': [40320, 720, 96]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{10}', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
