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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '960.1058', 'ambient_counter': 1058, 'ambient_order': 960, 'ambient_tex': 'C_{60}.\\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': False, 'core_order': 480, 'counter': 7, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.1058.2.e1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1.a1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '480.60', 'subgroup_hash': 60, 'subgroup_order': 480, 'subgroup_tex': 'C_{12}.D_{20}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.1058', 'aut_centralizer_order': 4, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': None, 'aut_weyl_index': 8, 'centralizer': '120.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.d1.a1', '4.e1.b1', '6.e1.a1', '10.e1.a1'], 'core': '2.e1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [7169, 3451, 7437, 2789, 8032, 6528, 7738, 6392], 'generators': [243, 320, 42, 480, 20, 16, 520], 'label': '960.1058.2.e1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.d1.a1', '4.e1.b1'], 'normalizer': '1.a1.a1', 'old_label': '2.e1.a1', 'projective_image': '120.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.e1.a1', 'subgroup_fusion': None, 'weyl_group': '120.42'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '16.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [2, 12, 12, 2, 4, 30, 4, 2], 'aut_gens': [[1, 8, 160], [17, 152, 320], [53, 380, 160], [99, 264, 160], [1, 12, 320], [117, 184, 320], [35, 408, 160], [53, 140, 160], [83, 8, 160]], 'aut_group': None, 'aut_hash': 5615892715607112017, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3840, 'aut_permdeg': 52, 'aut_perms': [76495334393332963371429646326033161742793603768641525187961401275054, 37233593802760068847845294582268631927563465133247917590837744471898, 78200296420015432131988428815915887495148336251390270492925492964684, 2450586352948192681800086568240, 20810450287947783226948592098195450072166699308439342294628393037527, 79082484871470180890275239819868966215610688151544570734135111701730, 37233593802760068847845294582268631923904727435037575747750210050978, 7854157153517572434627320844355313282294289094548327249662877649123], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [4, 6, 2, 2], [5, 2, 2, 1], [6, 2, 1, 3], [8, 10, 4, 1], [8, 30, 4, 1], [10, 2, 2, 3], [12, 2, 2, 2], [15, 4, 2, 1], [20, 2, 4, 2], [20, 6, 8, 2], [24, 10, 8, 1], [30, 4, 2, 3], [60, 4, 4, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5\\times S_3\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 1, 4], [4, 6, 4], [5, 2, 2], [6, 2, 3], [8, 10, 4], [8, 30, 4], [10, 2, 6], [12, 2, 4], [15, 4, 2], [20, 2, 8], [20, 6, 16], [24, 10, 8], [30, 4, 6], [60, 4, 8]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '60.8', 'commutator_count': 1, 'commutator_label': '30.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 60, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [4, 6, 1, 2], [4, 6, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [8, 10, 4, 1], [8, 30, 4, 1], [10, 2, 2, 3], [12, 2, 2, 2], [15, 4, 2, 1], [20, 2, 4, 2], [20, 6, 4, 2], [20, 6, 8, 1], [24, 10, 8, 1], [30, 4, 2, 3], [60, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 12, 'exponent': 120, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '60.8', 'hash': 60, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 10, 3], 'inner_gens': [[1, 152, 160], [17, 8, 320], [1, 328, 160]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'S_3\\times D_5', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 52], [4, 16]], 'label': '480.60', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 90, 'linQ_dim': 12, 'linQ_dim_count': 18, 'linR_count': 56, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12.D20', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 42, 'number_conjugacy_classes': 84, 'number_divisions': 33, 'number_normal_subgroups': 46, 'number_subgroup_autclasses': 72, 'number_subgroup_classes': 76, 'number_subgroups': 220, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 28], [5, 4], [6, 6], [8, 160], [10, 12], [12, 8], [15, 8], [20, 112], [24, 80], [30, 24], [60, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 8, 320], [5, 8, 160], [1, 12, 160], [3, 8, 160], [1, 136, 160]], 'outer_group': '64.260', 'outer_hash': 260, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [120, 39916800, 362880, 5040, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 8], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 10], [8, 10], [16, 3]], 'representations': {'PC': {'code': 13152503084638005831266143223821, 'gens': [1, 4, 7], 'pres': [7, -2, -2, -2, -2, -2, -5, -3, 14, 36, 4259, 80, 5044, 102, 5381, 1987]}, 'GLZN': {'d': 2, 'p': 60, 'gens': [216721, 6696031, 10692919, 10766331, 8929201, 6858916, 8856041]}, 'Perm': {'d': 20, 'gens': [6423390942797544, 1465, 194123381760, 2424, 288369849600, 3, 134470770610176000]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 8], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.D_{20}', 'transitive_degree': 480, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [20, 2, 4, 2, 4, 10, 4, 10, 4], 'aut_gens': [[1, 4, 80], [73, 764, 600], [67, 36, 560], [43, 764, 120], [3, 556, 80], [35, 748, 880], [51, 164, 440], [523, 764, 120], [17, 324, 400], [539, 908, 920]], 'aut_group': None, 'aut_hash': 2878935608206837536, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 30720, 'aut_permdeg': 64, 'aut_perms': [72096152218319763194413846335622169701432849974793164791973246443561082158965728107636547, 46230422833086147762410872437587317628062536876789288299703730394799871928179860572759638, 86698219863061864463949956772307108253834929313722702902941653255776428326748134082778930, 24503764658780828249480004638198867268001226556493649846773380391420766131413810935071318, 34426602524651933966846817428265162148085587922797502804512974260845833892804059733495946, 40348650841520989179326355389051702079536302338644405124268636477483376108770120043606972, 98719749662518242584394358096243375466381810285806558114373152153056910186720604202561330, 2109511833370973523519373713789273281493130702348465111600554567367782912668274688226186, 100578034516203641607522605554584411177698184837078290254324176112913859562158956642217599], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 2, 2], [4, 12, 2, 2], [5, 2, 2, 1], [6, 2, 1, 3], [8, 10, 4, 2], [8, 60, 4, 1], [10, 2, 2, 3], [12, 2, 2, 2], [12, 2, 4, 2], [15, 4, 2, 1], [20, 2, 4, 2], [20, 4, 4, 2], [20, 12, 8, 2], [24, 10, 8, 2], [30, 4, 2, 3], [60, 4, 4, 2], [60, 4, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{15}:(C_2^4\\times C_4\\times C_2^2\\wr C_2)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '128.2328', 'autcent_hash': 2328, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '240.195', 'autcentquo_hash': 195, 'autcentquo_nilpotent': False, 'autcentquo_order': 240, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [4, 1, 4], [4, 2, 4], [4, 12, 4], [5, 2, 2], [6, 2, 3], [8, 10, 8], [8, 60, 4], [10, 2, 6], [12, 2, 12], [15, 4, 2], [20, 2, 8], [20, 4, 8], [20, 12, 16], [24, 10, 16], [30, 4, 6], [60, 4, 24]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '120.42', 'commutator_count': 1, 'commutator_label': '60.13', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1058, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 12, 1, 4], [5, 2, 2, 1], [6, 2, 1, 3], [8, 10, 2, 2], [8, 10, 4, 1], [8, 60, 2, 2], [10, 2, 2, 3], [12, 2, 2, 4], [12, 2, 4, 1], [15, 4, 2, 1], [20, 2, 4, 2], [20, 4, 2, 2], [20, 4, 4, 1], [20, 12, 4, 4], [24, 10, 4, 2], [24, 10, 8, 1], [30, 4, 2, 3], [60, 4, 4, 4], [60, 4, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8064, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.42', 'hash': 1058, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 10, 6], 'inner_gens': [[1, 556, 80], [489, 4, 880], [1, 164, 80]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': False, 'inner_tex': 'S_3\\times D_{10}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 76], [4, 40]], 'label': '960.1058', 'linC_count': 256, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 160, 'linQ_dim': 14, 'linQ_dim_count': 104, 'linR_count': 176, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C60.OD16', 'ngens': 8, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 41, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 132, 'number_divisions': 52, 'number_normal_subgroups': 92, 'number_subgroup_autclasses': 136, 'number_subgroup_classes': 188, 'number_subgroups': 616, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 60], [5, 4], [6, 6], [8, 320], [10, 12], [12, 24], [15, 8], [20, 240], [24, 160], [30, 24], [60, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 48, 0, 33, 240, 0, 640], 'outer_gens': [[65, 876, 880], [531, 324, 880], [1, 364, 400], [491, 468, 440], [491, 956, 400], [67, 36, 560], [49, 868, 560]], 'outer_group': '256.56085', 'outer_hash': 56085, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 128, 'outer_perms': [351097902750379604218486221534484697977980164010593284793763401767121270741849152361175010791362963956842362486544990890745066915982850439711646269256295537497286396201654513108650979666294660912983445373938531084036, 302133512315038466322249626284334359905607566634712311383539666094550863928911153778598834926067187127066559363806920463754677662994837171763009402988293223455620632379547546430920557492303513664828706923779857924808, 121731523049591757171399962139285317322843057659047787546316948655353238493651211617696523445608431881356831924891299817872011684398648711918458623654692730712323672652263800153674375838813103965751548899721629632868, 181809100511571472789690411843685642329547132702322374479106986170123997770082255345924305065334414098367577512589561143962057318663860870788886683379475217974307862713989164922081166442799051154172210272124834831379, 236098172543862600973041185399884788058004621228876616121236372942085812193580332051018660836512151169710172517607476095497229672951564092158983607512734058086767144332170203848129452673748732801143035922561535973166, 6238830849388261225738111787484024626780325783776521903604353357026646180800595727352113773127806438126586706132302321160847682719802689001529260778371385374846014554555632571243417769407542888808407968214617318908, 328063424788676862063022317789069773867161228831717172978372823051994988536378051918600362961743347752722030713296533256096517590746074053319531652684614391255553082175019445897187448955988679782510430427941623930146], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4:C_2^5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 15], [8, 10], [16, 8], [32, 1]], 'representations': {'PC': {'code': 1440189201435277658658244178995965342911233458369, 'gens': [1, 3, 6], 'pres': [8, -2, -2, -2, -2, -5, -2, -2, -3, 16, 4169, 13346, 66, 2307, 91, 2564, 10581, 141, 11222, 166, 10263]}, 'Perm': {'d': 24, 'gens': [28207315932383002424424, 3425539190832582566401, 55083347176171961162880, 82261660440517189632000, 1321086775680, 55083347171874717696000, 3, 6504]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{60}.\\OD_{16}', 'transitive_degree': 960, '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}
