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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.10052', 'ambient_counter': 10052, 'ambient_order': 960, 'ambient_tex': 'C_4^2:S_3\\times C_{10}', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': True, 'core_order': 480, 'counter': 4, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.10052.2.c1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.c1', 'outer_equivalence': True, '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': ['F'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '480.919', 'subgroup_hash': 919, 'subgroup_order': 480, 'subgroup_tex': 'C_2\\times C_4\\times C_{60}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.10052', 'aut_centralizer_order': 24, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': None, 'aut_weyl_index': 24, 'centralizer': '2.c1', 'complements': ['480.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.h1', '6.a1', '10.c1'], 'core': '2.c1', 'coset_action_label': None, 'count': 1, 'diagramx': [1844, 7912, 5370, 1593], 'generators': [10, 40, 240, 320, 20, 480, 4], 'label': '960.10052.2.c1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.h1', '6.a1', '10.c1'], 'normalizer': '1.a1', 'old_label': '2.c1', 'projective_image': '12.4', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.c1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '480.919', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 4, 6], 'aut_gens': [[1, 2, 8], [245, 247, 13], [1, 242, 475], [1, 7, 111], [1, 121, 90]], 'aut_group': None, 'aut_hash': 8596656399186838937, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 12288, 'aut_permdeg': 30, 'aut_perms': [159163210500281568292638327290412, 155759454552747412435426033126130, 8848246704567947517120964212813, 63984318851403707379571767564554], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [3, 1, 2, 1], [4, 1, 24, 1], [5, 1, 4, 1], [6, 1, 6, 1], [6, 1, 8, 1], [10, 1, 12, 1], [10, 1, 16, 1], [12, 1, 48, 1], [15, 1, 8, 1], [20, 1, 96, 1], [30, 1, 24, 1], [30, 1, 32, 1], [60, 1, 192, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_4\\times C_2^6.S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': None, 'autcent_hash': 8596656399186838937, 'autcent_nilpotent': False, 'autcent_order': 12288, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times C_4\\times C_2^6.S_4', '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, 7], [3, 1, 2], [4, 1, 24], [5, 1, 4], [6, 1, 14], [10, 1, 28], [12, 1, 48], [15, 1, 8], [20, 1, 96], [30, 1, 56], [60, 1, 192]], 'center_label': '480.919', 'center_order': 480, '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', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 919, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 2], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 12], [5, 1, 4, 1], [6, 1, 2, 7], [10, 1, 4, 7], [12, 1, 4, 12], [15, 1, 8, 1], [20, 1, 8, 12], [30, 1, 8, 7], [60, 1, 16, 12]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 2821, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.47', 'hash': 919, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 8], [1, 2, 8], [1, 2, 8]], '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, 480]], 'label': '480.919', 'linC_count': None, 'linC_degree': 3, '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': 'C2*C4*C60', 'ngens': 7, 'nilpotency_class': 1, 'nilpotent': True, '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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 480, 'number_divisions': 80, 'number_normal_subgroups': 216, 'number_subgroup_autclasses': 48, 'number_subgroup_classes': 216, 'number_subgroups': 216, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [5, 4], [6, 14], [10, 28], [12, 48], [15, 8], [20, 96], [30, 56], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [4, 4, 3, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[5, 124, 134], [1, 363, 380], [241, 360, 254], [245, 120, 227]], 'outer_group': None, 'outer_hash': 8596656399186838937, 'outer_nilpotent': False, 'outer_order': 12288, 'outer_permdeg': 30, 'outer_perms': [118014485420116202904712819931342, 219182020528196612718537792691205, 72890964295058794160865053486462, 73811293597240036471345672796639], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times C_4\\times C_2^6.S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 20], [8, 20], [16, 12]], 'representations': {'PC': {'code': 245743619577238945799, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -5, 36, 80, 102, 166]}, 'GLZN': {'d': 2, 'p': 40, 'gens': [1088017, 2513229, 576009, 2312611, 1344021, 192003, 64321]}, 'Perm': {'d': 18, 'gens': [4097379686400, 127008000, 355687428096000, 10080, 96, 1313901388800, 40279680]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 60], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4\\times C_{60}', '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': '160.228', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [4, 4, 8, 4, 12, 12], 'aut_gens': [[1, 2, 20, 80], [851, 58, 60, 900], [811, 486, 540, 410], [521, 526, 550, 940], [851, 54, 30, 460], [161, 538, 70, 600], [851, 534, 500, 580]], 'aut_group': None, 'aut_hash': 4741775015152245913, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 98304, 'aut_permdeg': 44, 'aut_perms': [2186748863410372259383286755034091770325609770567878754, 1170935976181801035701944328046195838723281219565495017, 527904328706537419854160969707650194761274480894723957, 2186749067775327149769595444301650445466398101820217962, 179472054180061413719841387545286758501878320942706440, 2228290890191264784110336356454495775608987558313545273], 'aut_phi_ratio': 384.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 1, 4, 1], [2, 6, 4, 1], [3, 2, 1, 1], [4, 1, 8, 1], [4, 2, 8, 1], [4, 6, 4, 1], [4, 6, 8, 1], [5, 1, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 2, 4, 1], [10, 1, 4, 1], [10, 1, 8, 1], [10, 1, 16, 1], [10, 6, 16, 1], [12, 2, 8, 1], [12, 2, 16, 1], [15, 2, 4, 1], [20, 1, 32, 1], [20, 2, 32, 1], [20, 6, 16, 1], [20, 6, 32, 1], [30, 2, 4, 1], [30, 2, 8, 1], [30, 2, 16, 1], [60, 2, 32, 1], [60, 2, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^5.C_2^5.C_2^5)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 8, 'autcent_group': None, 'autcent_hash': 3230402273819117835, 'autcent_nilpotent': True, 'autcent_order': 16384, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6.C_2^3.C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 6, 4], [3, 2, 1], [4, 1, 8], [4, 2, 8], [4, 6, 12], [5, 1, 4], [6, 2, 7], [10, 1, 28], [10, 6, 16], [12, 2, 24], [15, 2, 4], [20, 1, 32], [20, 2, 32], [20, 6, 48], [30, 2, 28], [60, 2, 96]], 'center_label': '80.45', 'center_order': 80, 'central_product': True, 'central_quotient': '12.4', 'commutator_count': 1, 'commutator_label': '6.2', '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': 10052, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1], ['96.79', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 6, 1, 4], [3, 2, 1, 1], [4, 1, 2, 4], [4, 2, 2, 4], [4, 6, 1, 4], [4, 6, 2, 4], [5, 1, 4, 1], [6, 2, 1, 7], [10, 1, 4, 7], [10, 6, 4, 4], [12, 2, 2, 4], [12, 2, 4, 4], [15, 2, 4, 1], [20, 1, 8, 4], [20, 2, 8, 4], [20, 6, 4, 4], [20, 6, 8, 4], [30, 2, 4, 7], [60, 2, 8, 4], [60, 2, 16, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2555280, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '240.206', 'hash': 10052, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 1, 1, 6], 'inner_gens': [[1, 2, 20, 440], [1, 2, 20, 80], [1, 2, 20, 80], [681, 2, 20, 80]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 12, 'inner_split': False, 'inner_tex': 'D_6', 'inner_used': [1, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 160], [2, 200]], 'label': '960.10052', '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': 'C4^2:S3*C10', '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': 30, 'number_characteristic_subgroups': 34, 'number_conjugacy_classes': 360, 'number_divisions': 88, 'number_normal_subgroups': 334, 'number_subgroup_autclasses': 184, 'number_subgroup_classes': 660, 'number_subgroups': 1392, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 31], [3, 2], [4, 96], [5, 4], [6, 14], [10, 124], [12, 48], [15, 8], [20, 384], [30, 56], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [4, 4, 8, 4, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 320, 640], 'outer_gens': [[851, 58, 60, 900], [811, 486, 540, 410], [521, 526, 550, 940], [851, 54, 30, 460], [161, 538, 70, 600], [851, 534, 500, 580]], 'outer_group': None, 'outer_hash': 6714790469588492835, 'outer_nilpotent': True, 'outer_order': 8192, 'outer_permdeg': 256, 'outer_perms': [3430266600048808168769762230461324084304721731796304436557936479750989055006706905230964183020788839413883561249421806916805436894902230948229053420470200786715120354369643968868273454382107934220806122978808001455966490734076646502184340149169410654473995867580022774518339348921790489728997137100808016613802468845129944246517240898119639186924104133344385540342606507891602545009718853097498181354153873620782359447197317931647615238534425190733779509360513458401080813538250119691796003537244054897768, 6794309815747679338795561501236053836024142671106704092491684452709211943775332870636765585214797802405525535026194861505364016876041894290145431861280013135531883042670253779891863965801499008932310530841924305467750205504913667599046543388548083083426237771245140473746812917749028425075085575457182407112289419080038640674718453333436557285242364936223138044608002734741725367753583306739677546029433282703243031135530552425322048199723215955204095463417114325633139231779492774914681215104661331089505, 10158353031572631895667500703994909616309178236273590404212457104713311291633064671195226794058049455139324959457441828202380526388416899975314381296015201577260506228464280274959055216884930073378541858264711150373236257171036230785695534325985607405605020853649861586982600367085002742155649626633050400150075237350623899248917838638300968653423677686761355111372185582124419143517324244942825484983721095251618318189145348164854414935189575947552834911486704211163599833646190476814512302955697713473670, 13522396247336160198031274660726964683065564923200124308351582075547822103465127680836213069657272521244973825215382631210574524909210684164397629173205356224815399155052422923197365606269095486056163189479977942152670517428224287964368066272253550871206255834772794418456345251181324865799991163254471811640521734259113619900448917659063008489355767370743484991427596342082850329845295906730182375429757624626696576924825522162381404615701932053969574491086556092356521084176161531004956348472693372799310, 16886439463005935661709002246107990647569551150342948893882124503796329184421579428822425909902267011255634113858432390053956808364916513512072739241123939869827771078801566322977982660548992181774243425564055625697822782323573732993326437228097645095560116056651343438032655002336313935958388062394955401064011725659539269602759803540515439326453453231693803646964251014956031857762793711265974071573755246756289647880937284825270485332018339979803084424022902491396751417299643069512823530536314018702780, 20250482678859983927232622503179758530321372477282221916349748518676851206628001794856039734996374118615444577825135680431480507202401706391335069931705737192572212695838471168525534739742466976049448859763029937600773988989068004727409176032024581115245277899914772918700622421638406756072102546582314782369770407252408125014311379101221868512595299928425363760080570426267442700562393719116646315093367209337932314939803201640811961981135184306102933841017700689963665392159491985225094040603428028021161], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4.C_2^5.C_2^4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4, 5], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 16], [4, 24], [8, 20], [16, 8], [32, 4]], 'representations': {'PC': {'code': 1766310822433241266427578932661249, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -5, -2, -2, 2, -2, -3, 41, 91, 21125, 141, 44806, 166, 40967]}, 'GLZN': {'d': 2, 'p': 88, 'gens': [1193611, 30666285, 30843451, 6133257, 45658691, 685345, 49875609, 40598257]}, 'Perm': {'d': 22, 'gens': [51347038428091930320, 109506243016029525840, 163626575012832597120, 166059456098223703680, 33, 109506243016029525120, 109506243016025856000, 6706022400]}}, 'schur_multiplier': [2, 2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:S_3\\times C_{10}', 'transitive_degree': 480, '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}
