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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '400.212', 'ambient_counter': 212, 'ambient_order': 400, 'ambient_tex': 'C_2\\times C_5^2:Q_8', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 200, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '400.212.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '200.44', 'subgroup_hash': 44, 'subgroup_order': 200, 'subgroup_tex': 'C_5^2:Q_8', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '400.212', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '2400.dc', 'aut_weyl_index': 4, 'centralizer': '200.a1.a1', 'complements': ['200.c1.a1', '200.a1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.c1', '4.b1.f1', '50.b1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [7744, 1380, 1034, 3611, 8900, 1287, 6803, 3508], 'generators': [1533752, 547501, 1797504, 391271, 1940071], 'label': '400.212.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.c1', '4.b1.f1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '400.212', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '200.44'}
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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': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [4, 6, 4, 4, 5, 5], 'aut_gens': [[1563129, 1047513, 547511, 625626, 1940071], [1875649, 783778, 703771, 391266, 1627551], [1797519, 486964, 469396, 625631, 1252602], [1563129, 813133, 625631, 469376, 486964], [1641254, 1531892, 469381, 547506, 1783806], [1563144, 813148, 547511, 625626, 1861931], [1797524, 813143, 547511, 625626, 1705686]], 'aut_group': '2400.dc', 'aut_hash': 4785015580083470286, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2400, 'aut_permdeg': 25, 'aut_perms': [6483096545327141231207316, 12772161008222244511512321, 13317945288467576888268300, 10919564784166816960418121, 13176395421532501323010424, 10618923126478059764371593], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [4, 50, 3, 1], [5, 8, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5^2:\\Unitary(2,3)', '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': 120, 'autcentquo_group': '2400.dc', 'autcentquo_hash': 4785015580083470286, 'autcentquo_nilpotent': False, 'autcentquo_order': 2400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_5^2:\\Unitary(2,3)', 'cc_stats': [[1, 1, 1], [2, 25, 1], [4, 50, 3], [5, 8, 3]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '200.44', 'commutator_count': 1, 'commutator_label': '50.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 44, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 25, 1, 1], [4, 50, 1, 3], [5, 8, 1, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 6, 'exponent': 20, 'exponents_of_order': [3, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 1, 3]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '200.44', 'hash': 44, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 5, 5, 4], 'inner_gens': [[1563129, 969393, 625641, 547501, 1705681], [1563139, 1047513, 547521, 703751, 643219], [1641259, 1125633, 547511, 625626, 1783811], [1875629, 891263, 547511, 625626, 1940051], [1875649, 1219382, 469381, 547506, 1940071]], 'inner_hash': 44, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'C_5^2:Q_8', 'inner_used': [1, 2, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 4], [2, 1], [8, 3]], 'label': '200.44', 'linC_count': 3, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 3, 'linQ_dim': 8, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C5^2:Q8', 'ngens': 5, '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': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 8, 'number_divisions': 8, 'number_normal_subgroups': 7, 'number_subgroup_autclasses': 11, 'number_subgroup_classes': 21, 'number_subgroups': 198, 'old_label': None, 'order': 200, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 25], [4, 150], [5, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [4, 3], 'outer_gen_pows': [391251, 391251], 'outer_gens': [[1797524, 783793, 625641, 391256, 1861946], [1641269, 1627571, 391266, 547511, 861913]], 'outer_group': '12.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 7, 'outer_perms': [137, 1440], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_3:C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 1], [8, 3]], 'representations': {'PC': {'code': 132072424478758488409590799, 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -2, -5, 5, 20, 61, 26, 483, 568, 173, 2604, 1509, 1014]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1563129, 1047513, 547511, 625626, 1940071]}, 'Perm': {'d': 10, 'gens': [2177160, 50413, 131783, 816576, 1451584]}}, 'schur_multiplier': [5], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5^2:Q_8', 'transitive_degree': 10, '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 120, 'aut_gen_orders': [4, 6, 4, 4, 10, 10], 'aut_gens': [[1563129, 1047513, 547511, 625626, 485084, 1565004], [1563144, 1094423, 625641, 625636, 1627566, 1565004], [1719394, 1860066, 391256, 469386, 940028, 1565004], [1875629, 1047523, 547521, 703751, 408839, 1565004], [1719389, 1127513, 703766, 469391, 408844, 1565004], [1719389, 813128, 547511, 625626, 1627551, 1565004], [1641274, 1533762, 547511, 625626, 1705696, 1565004]], 'aut_group': '9600.cj', 'aut_hash': 3817808798694075455, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9600, 'aut_permdeg': 300, 'aut_perms': [167493682713716141535363778230418558506478090995736444466475019213583991949326890132650945800385029030422406780294901207386933531146606511302522233932408947975766604752497719567694928964975201122822216377387269930842299989480801886137209887615743454946199567379673903545382323862117842852867465461654630689020203718449853399428374366021588465671347351733081686934834506835126873019208127472690870565183525363765923237294052035427827827931741161433804771240906675072197264006351261577964340968904124615163007639878744327485590280373534902946145587143835348507014514300208409723329484034485949127134337011355710405602, 156824106101552189569596725151149496872263924754245970169166286756072220370259049320687787727101561804218243118552729394757160065271599522769284691727808592617413992890830471430027004400508449133919899751850867935427674881245069553259876710745236267866588968833664358257755736990032682084093111889791760595008176741461956316424788654558184657858189321494198101538736334596057862396640312226712780054132303580753666805443271118262827959217459794634568895120340723619341871054249427894730840235190988359707349811431154600273279856564711127528896537263165849944579683212406674623798663141146508295020939017956997761379, 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116261026189454223639016669902638616392597425933159205068297487325996653874058449762449367089715543510566479761194730223095365896282595793859453885495582205266308581473080175148163445015877908047026312022407737808982978464645805115709305268520604783270879622982705333644454132011938374988309472133717503293604334765136059322864625050785859047907097191648408612760504022067662820388681679480575504679534002999628857984276661194099158476863758276619088753681151152083362208224241519753643029918439038359297426113481168510106031748885784523980422057193737180847292250885600521441163130062055598831998124410808714216608, 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7005568427563872532557559838090249180067565987727272988316477599022383837591601542738291199812692742196739125524088827102565354471304206888702017290413778031237292139961897643635919527226352867095575349585023792637027311399177634037614582429327763033881954967682822963749984894817606194823161441728122898015134091198822385017207389602456633424040318050827068047930331813259659507180568329513291670968775020083927780354558935224337816191546789092445963992526983585098435089135697575567869556202123969310627059727613048075468788765894837293060247633891409674555421226537497658186598218564664182528970635049720049504], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 1, 2], [4, 50, 6, 1], [5, 8, 3, 1], [10, 8, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{10}^2:\\Unitary(2,3)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 120, 'autcentquo_group': '2400.dc', 'autcentquo_hash': 4785015580083470286, 'autcentquo_nilpotent': False, 'autcentquo_order': 2400, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_5^2:\\Unitary(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 25, 2], [4, 50, 6], [5, 8, 3], [10, 8, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '200.44', 'commutator_count': 1, 'commutator_label': '50.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 212, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['200.44', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 25, 1, 2], [4, 50, 1, 6], [5, 8, 1, 3], [10, 8, 1, 3]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 2184, 'exponent': 20, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 5], 'faithful_reps': [[8, 1, 3]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '400.212', 'hash': 212, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 20, 'inner_gen_orders': [2, 4, 5, 5, 4, 1], 'inner_gens': [[1563129, 969393, 625641, 547501, 719474, 1565004], [1563139, 1047513, 547521, 703751, 1781936, 1565004], [1641259, 1125633, 547511, 625626, 641344, 1565004], [1875629, 891263, 547511, 625626, 485079, 1565004], [1875649, 1219382, 469381, 547506, 485084, 1565004], [1563129, 1047513, 547511, 625626, 485084, 1565004]], 'inner_hash': 44, 'inner_nilpotent': False, 'inner_order': 200, 'inner_split': False, 'inner_tex': 'C_5^2:Q_8', 'inner_used': [1, 2, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 2], [8, 6]], 'label': '400.212', 'linC_count': 3, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 3, 'linQ_dim': 8, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*C5^2:Q8', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 16, 'number_divisions': 16, 'number_normal_subgroups': 21, 'number_subgroup_autclasses': 25, 'number_subgroup_classes': 62, 'number_subgroups': 638, 'old_label': None, 'order': 400, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 51], [4, 300], [5, 24], [10, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [6, 2, 4, 2, 2], 'outer_gen_pows': [1797504, 391251, 391251, 1797504, 1797504], 'outer_gens': [[1719399, 1627566, 391271, 469381, 1406982, 1565004], [1641254, 1125643, 625641, 547501, 1705676, 1565004], [1719379, 891263, 391261, 469376, 1406987, 1565004], [1719379, 1221257, 703771, 469376, 1861931, 1565004], [1875629, 969383, 469381, 703751, 641339, 1565004]], 'outer_group': '48.30', 'outer_hash': 30, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 8, 'outer_perms': [15247, 11520, 1577, 16687, 7], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'A_4:C_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [8, 6]], 'representations': {'PC': {'code': 216906891399430122331435370165027794006067, 'gens': [1, 2, 4, 5], 'pres': [6, 2, 2, 2, 5, 2, 5, 24, 73, 31, 4227, 4233, 207, 3604, 730, 2716, 88, 8645, 1739, 2897]}, 'GLFp': {'d': 3, 'p': 5, 'gens': [1563129, 1047513, 547511, 625626, 485084, 1565004]}, 'Perm': {'d': 12, 'gens': [945727, 41027094, 1, 1588326, 7827270, 85333680]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_5^2:Q_8', 'transitive_degree': 20, 'wreath_data': None, 'wreath_product': False}
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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}
