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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '52272.a', 'ambient_counter': 1, 'ambient_order': 52272, 'ambient_tex': 'C_{396}.D_{66}', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 66, 'counter': 675, 'cyclic': True, 'direct': None, 'hall': 0, 'label': '52272.a.792._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '792.B', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '792.42', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, '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': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '66.4', 'subgroup_hash': None, 'subgroup_order': 66, 'subgroup_tex': 'C_{66}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '52272.a', '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': [2189977418, 17081821302, 2127406644], 'label': '52272.a.792._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '792.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '792._.B', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '66.4', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 10, 'aut_gen_orders': [2, 10], 'aut_gens': [[1], [43], [53]], 'aut_group': '20.5', 'aut_hash': 5, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 20, 'aut_permdeg': 9, 'aut_perms': [720, 40353], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [11, 1, 10, 1], [22, 1, 10, 1], [33, 1, 20, 1], [66, 1, 20, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2\\times C_{10}', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 10, 'autcent_group': '20.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 20, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{10}', '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], [3, 1, 2], [6, 1, 2], [11, 1, 10], [22, 1, 10], [33, 1, 20], [66, 1, 20]], 'center_label': '66.4', 'center_order': 66, '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', '3.1', '11.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1], [11, 1, 10, 1], [22, 1, 10, 1], [33, 1, 20, 1], [66, 1, 20, 1]], 'element_repr_type': 'PC', 'elementary': 66, 'eulerian_function': 1, 'exponent': 66, 'exponents_of_order': [1, 1, 1], 'factors_of_aut_order': [2, 5], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[1, 0, 20]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '66.4', 'hash': 4, 'hyperelementary': 66, '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': 20, 'irrQ_dim': 20, 'irrR_degree': 2, 'irrep_stats': [[1, 66]], 'label': '66.4', 'linC_count': 20, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 3, 'linQ_dim': 12, 'linQ_dim_count': 3, 'linR_count': 10, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C66', 'ngens': 3, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 66, 'number_divisions': 8, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 8, 'number_subgroups': 8, 'old_label': None, 'order': 66, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2], [11, 10], [22, 10], [33, 20], [66, 20]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [2, 10], 'outer_gen_pows': [0, 0], 'outer_gens': [[43], [53]], 'outer_group': '20.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 20, 'outer_permdeg': 9, 'outer_perms': [720, 40353], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 11], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2], [10, 2], [20, 2]], 'representations': {'PC': {'code': 2467019, 'gens': [1], 'pres': [3, -2, -3, -11, 6, 22]}, 'GLFp': {'d': 2, 'p': 23, 'gens': [160116]}, 'Perm': {'d': 16, 'gens': [1307674368000, 12454041600, 36288000]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [66], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{66}', 'transitive_degree': 66, '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': '792.45', '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, 30, 60, 30, 30, 60], 'aut_gens': [[312853870, 3378821867, 158006], [20210360002, 4379954490, 19925033], [11387880868, 7821346679, 46410491], [12076159382, 3316250984, 21549557], [12076159382, 21399204532, 1320025], [23526611024, 8134200603, 17861427], [3191109474, 11575593299, 32509536], [23464040250, 20585784533, 60098257], [15142127308, 11575593299, 24831953]], 'aut_group': None, 'aut_hash': 8053056455156274175, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 633600, 'aut_permdeg': 150, 'aut_perms': [30571246183157538195717985717383337899364115750550513138399566675861252952431507043265190030222473550258703414840449478973484119889100800939498650052081542944045756285110067852289982291460093022050428406058839027291874763438453832601413882042429979142623618360241, 47584153189573605927825520239616468041079273620158819120610750786011174594176908492771406002866788292945938642317037628344109948701517754893791759855569504027032918231739850452138515221162874467074829324062994222655786907499896439633946708236983128778616040299498, 4011747499079041964464934733387172377663687494093935349986440924137643967349258357570333044057306233622797442881230580082087434330102887523650207277298276888296622767890542440389832768247644854519082286439307513613813721806987937206428424227612544739608746435074, 13042915107735963963184161364763780057132121039451834660700402711823769652723398180502684896311653069914256910841086306650945213015187063208085993373781475676395913735842734798806075945896394039286264813450397261284729014816235930248517452791333881130619903721191, 29702854274381241220883988343886876550730530301671422555473871710913247113273440644014975451951870132812961503758091894557185523845774906678562063407218969377366271080699781154394596266971976828098306992332734704973823133465966021798295628290285466279539276329243, 41639147581641237590329131562861522645646787023157625686644735521207476484697183060987631709972504969704700684641676654893801491177533388276756514167059479579104135635958499656386629480385900483605741078321342742662384317773400255990315448593634611090641299265384, 37391129615261399434442739508511510818536953236556801062368185231256151024055596660297487185793130659171334372539599874940242263287453823218319686068768984004137911742202593377336634927816975786436654708345274190163791320568632952199046399053334113202556097882751, 56636713476339664782260208210486774023763234999318105767068404377760927041879229706794658965952436997315320534582349073870971174080950139378710256015860958732256903303461406073965032036740565437443072412366289008519815843544686956841844567389249072795258744260457], 'aut_phi_ratio': 40.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 66, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 66, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 3], [6, 2, 4, 1], [6, 66, 4, 1], [9, 1, 6, 1], [9, 2, 6, 1], [11, 1, 10, 1], [11, 2, 5, 1], [11, 2, 50, 1], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 66, 4, 1], [18, 1, 6, 1], [18, 2, 6, 2], [18, 2, 12, 1], [18, 66, 12, 1], [22, 1, 10, 1], [22, 2, 5, 1], [22, 2, 10, 2], [22, 2, 50, 1], [22, 2, 100, 1], [22, 66, 20, 1], [33, 1, 20, 1], [33, 2, 10, 3], [33, 2, 20, 2], [33, 2, 100, 2], [33, 2, 200, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 66, 12, 1], [44, 1, 20, 1], [44, 2, 10, 3], [44, 2, 100, 2], [44, 66, 20, 1], [66, 1, 20, 1], [66, 2, 10, 3], [66, 2, 20, 6], [66, 2, 40, 2], [66, 2, 100, 2], [66, 2, 200, 3], [66, 2, 400, 1], [66, 66, 40, 1], [99, 1, 60, 1], [99, 2, 30, 1], [99, 2, 60, 2], [99, 2, 300, 1], [99, 2, 600, 1], [132, 1, 40, 1], [132, 2, 20, 7], [132, 2, 40, 4], [132, 2, 200, 4], [132, 2, 400, 2], [132, 66, 40, 1], [198, 1, 60, 1], [198, 2, 30, 1], [198, 2, 60, 4], [198, 2, 120, 2], [198, 2, 300, 1], [198, 2, 600, 2], [198, 2, 1200, 1], [198, 66, 120, 1], [396, 1, 120, 1], [396, 2, 60, 3], [396, 2, 120, 4], [396, 2, 600, 2], [396, 2, 1200, 2], [396, 66, 120, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{330}.C_{30}.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 30, 'autcent_group': '480.1213', 'autcent_hash': 1213, 'autcent_nilpotent': True, 'autcent_order': 480, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4\\times C_{30}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '1320.142', 'autcentquo_hash': 142, 'autcentquo_nilpotent': False, 'autcentquo_order': 1320, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 66, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 1], [4, 66, 2], [6, 1, 2], [6, 2, 11], [6, 66, 4], [9, 1, 6], [9, 2, 6], [11, 1, 10], [11, 2, 55], [12, 1, 4], [12, 2, 14], [12, 66, 4], [18, 1, 6], [18, 2, 24], [18, 66, 12], [22, 1, 10], [22, 2, 175], [22, 66, 20], [33, 1, 20], [33, 2, 470], [36, 1, 12], [36, 2, 30], [36, 66, 12], [44, 1, 20], [44, 2, 230], [44, 66, 20], [66, 1, 20], [66, 2, 1430], [66, 66, 40], [99, 1, 60], [99, 2, 1050], [132, 1, 40], [132, 2, 1900], [132, 66, 40], [198, 1, 60], [198, 2, 3210], [198, 66, 120], [396, 1, 120], [396, 2, 4260], [396, 66, 120]], 'center_label': '396.4', 'center_order': 396, 'central_product': None, 'central_quotient': '132.9', 'commutator_count': None, 'commutator_label': '66.4', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '11.1', '11.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 66, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 66, 1, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 66, 2, 2], [9, 1, 6, 1], [9, 2, 6, 1], [11, 1, 10, 1], [11, 2, 5, 1], [11, 2, 10, 5], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 66, 2, 2], [18, 1, 6, 1], [18, 2, 6, 4], [18, 66, 6, 2], [22, 1, 10, 1], [22, 2, 5, 1], [22, 2, 10, 17], [22, 66, 10, 2], [33, 1, 20, 1], [33, 2, 10, 3], [33, 2, 20, 22], [36, 1, 12, 1], [36, 2, 6, 1], [36, 2, 12, 2], [36, 66, 6, 2], [44, 1, 20, 1], [44, 2, 10, 3], [44, 2, 20, 10], [44, 66, 10, 2], [66, 1, 20, 1], [66, 2, 10, 3], [66, 2, 20, 70], [66, 66, 20, 2], [99, 1, 60, 1], [99, 2, 30, 1], [99, 2, 60, 17], [132, 1, 40, 1], [132, 2, 20, 7], [132, 2, 40, 44], [132, 66, 20, 2], [198, 1, 60, 1], [198, 2, 30, 1], [198, 2, 60, 53], [198, 66, 60, 2], [396, 1, 120, 1], [396, 2, 60, 3], [396, 2, 120, 34], [396, 66, 60, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 396, 'exponents_of_order': [4, 3, 2], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': None, 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': None, 'hash': 7262420344290648285, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [1, 66, 2], 'inner_gens': [[312853870, 3378821867, 158006], [312853870, 3378821867, 22434867], [312853870, 7821346679, 158006]], 'inner_hash': 9, 'inner_nilpotent': False, 'inner_order': 132, 'inner_split': True, 'inner_tex': 'D_{66}', 'inner_used': [2, 3], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '52272.a', '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': 'C396.D66', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 2, 3, 2, 1, 2, 2, 6, 0, 2, 2, 2, 1, 4, 6, 6, 0, 1, 4, 2, 2, 4, 3, 1, 16, 0, 0, 4, 1, 1, 10, 2, 2, 16, 0, 3, 1, 2, 2, 10, 1, 2, 10, 10, 1, 0, 2, 8, 8, 1, 10, 1, 1, 1, 8, 7, 1, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 132, 'number_characteristic_subgroups': 162, 'number_conjugacy_classes': 13662, 'number_divisions': 360, 'number_normal_subgroups': 210, 'number_subgroup_autclasses': None, 'number_subgroup_classes': 944, 'number_subgroups': 5440, 'old_label': None, 'order': 52272, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 135], [3, 8], [4, 136], [6, 288], [9, 18], [11, 120], [12, 296], [18, 846], [22, 1680], [33, 960], [36, 864], [44, 1800], [66, 5520], [99, 2160], [132, 6480], [198, 14400], [396, 16560]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [30, 30, 10, 10, 30, 30, 10], 'outer_gen_pows': [3941959033, 62570774, 62570774, 62570774, 62570774, 62570774, 3941959033], 'outer_gens': [[9761040744, 3316250984, 52666417], [15454981178, 8134200603, 158006], [14891844212, 23902035630, 158006], [16456113562, 5381086815, 158006], [4630237276, 7070497479, 52666417], [23464040250, 1063703468, 158006], [5005661920, 10386748660, 52666417]], 'outer_group': None, 'outer_hash': 3046548263567564668, 'outer_nilpotent': True, 'outer_order': 4800, 'outer_permdeg': 25, 'outer_perms': [2439325392370675200, 620448401733239959488064, 620448408135613146297600, 6423296496025050, 1126440053082800064090, 620448401754249927909184, 620450834635247616409050], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_{10}\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 42, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 9, 11], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '332428954397036115511298492385121536913932833142137054000119019', 'gens': [1, 2, 7], 'pres': [9, 2, 2, 2, 3, 3, 11, 2, 3, 11, 46, 74, 138, 175, 3280290, 186, 3677191, 286, 3878288]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [312853870, 3378821867, 158006]}, 'Perm': {'d': 42, 'gens': [33494892189173938695643869461138871064028370821298, 68600184037293979860939412545269481844910428311020, 69414557780178293883813031121179557779606504440859]}}, 'schur_multiplier': [2, 2], 'semidirect_product': False, 'simple': False, 'smith_abelian_invariants': [2, 2, 198], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{396}.D_{66}', '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}
