-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '972.755', 'ambient_counter': 755, 'ambient_order': 972, 'ambient_tex': 'C_{12}.C_3^4', 'central': False, 'central_factor': True, 'centralizer_order': 12, 'characteristic': True, 'core_order': 486, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '972.755.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', '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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '486.254', 'subgroup_hash': 254, 'subgroup_order': 486, 'subgroup_tex': 'C_6.C_3^4', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '972.755', 'aut_centralizer_order': 2, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '8398080.j', 'aut_weyl_index': 2, 'centralizer': '81.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '6.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [6154, 3337, 2932, 3117], 'generators': [486, 9, 324, 1, 3, 27], 'label': '972.755.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '162.55', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '81.15'}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '162.55', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 360, 'aut_gen_orders': [3, 3, 3, 3, 18, 24], 'aut_gens': [[24577758, 2939606, 1017496, 25633100, 28816400, 13886268], [32864349, 43014227, 1017496, 8194004, 28816400, 13886268], [32864349, 43014227, 1017496, 25633100, 28816400, 34888062], [7138662, 20201582, 40442506, 8194004, 28816400, 13886268], [32864349, 43014227, 1017496, 8194004, 28816400, 17389827], [31020225, 22054463, 40661731, 12623919, 28816400, 21276646], [31289712, 21835277, 36462699, 40661731, 28816400, 10956204]], 'aut_group': '8398080.j', 'aut_hash': 1287654720189540806, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8398080, 'aut_permdeg': 242, 'aut_perms': [17020440852079934851897528077496566761022955571111615055277677487054344436181863182238709538731356507650199809120325522561297865361357238516586897341395993430058326605392949914944894741420556295076069782330170342903746091484555512433475168649467147975260281903380294250379952284149631249961701464100638390108194090800039316490586367562553912116607245458832088682772780800668635577154232068181290731722455479867656909938168669949112393694973431863382366227439061529747, 33899047211631958627188631579939761768881020073031884806421250434407959166233121194786558445329756930833420963616328214595666604404583658533145708373712031533997318917771606384631578468688647419063406442124511950555711816993726577734295066402610391642104295914390962196474313836671358466513234913883359704226407617365257775446683932897085339663203535491621500861918502421658669237599115386175980787522550509544332557813647054625503895278216799085917707564132628582400, 17020442114693941943705892634949164688547621163221495625355156547479698255876464076025930980718029403338627808176948218428217299754151167977139936801977585873912715327485019689612514551137993149658390603819423535258909742796303800638734830748686312865557042295032233593893411632986319111783600205240397683397465493139416880976657278514111893999628936402403558218463676776912616755493670030858651750448669997408843918300799702718777395325168837553742716441630519405360, 97296796852044310149705414943571480755545681455733510159809448235063526364630927090848798812450636316347071491356726668992175146080030340751367679273372164829871924109698066510895327834863598508577152961974639582145088740727511793050749475874056930961413793019713087020618509921301134344689928839718435255543145327042795022799071105769129097856486447326008708247705816804246840830319546775226518062766055018806651161587695604890980483029047665099472787, 2416873905575856983533447707462606330113732788972471488675948317162764235175132632590641734798437893214609995349155371584373570906077782126282372429328083580970109151917318300847581118158055916375346824383100314866636107399714564822925196011819471425922794461993153522092982390469956634982996816601222975102749934482797419005971693571850121472994869326597657578148796765520055976261773024363958411082523913290867258693601853787510004544894582375995432655022676929752442, 982658172446505800054250517276354967450729866927132781393613306557456959064423875726086889562025718636226096461667763108759222048214435021912618414146702379611282957674304754475391322127719572693498471113453639420415169661307109379038051902171226033448350573646549318502115002969996766940284098324102046683466130011330428262453296982265970679485463182752242487820305700168009642364413617454291873203389570196846144879266565870352174105888049048942260965548802988527250934], 'aut_phi_ratio': 51840.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 80, 1], [6, 1, 2, 1], [6, 3, 80, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:S_3.\\SO(5,3)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 3, 'autcent_group': '81.15', 'autcent_hash': 15, 'autcent_nilpotent': True, 'autcent_order': 81, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 360, 'autcentquo_group': '103680.b', 'autcentquo_hash': 1958447605843920035, 'autcentquo_nilpotent': False, 'autcentquo_order': 103680, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\GSp(4,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 3, 80], [6, 1, 2], [6, 3, 80]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '81.15', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 254, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['243.65', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 2, 40], [6, 1, 2, 1], [6, 3, 2, 40]], 'element_repr_type': 'GLFp', 'elementary': 3, 'eulerian_function': 3510, 'exponent': 6, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 2]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '162.55', 'hash': 254, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [3, 3, 3, 3, 1, 3], 'inner_gens': [[24577758, 2939606, 1017496, 25633100, 28816400, 34888062], [24577758, 2939606, 1017496, 25633100, 28816400, 17389827], [24577758, 2939606, 1017496, 8194004, 28816400, 34888062], [24577758, 2939606, 23121499, 25633100, 28816400, 13886268], [24577758, 2939606, 1017496, 25633100, 28816400, 13886268], [7138662, 20201582, 23121499, 25633100, 28816400, 13886268]], 'inner_hash': 15, 'inner_nilpotent': True, 'inner_order': 81, 'inner_split': True, 'inner_tex': 'C_3^4', 'inner_used': [1, 3, 4, 6], 'irrC_degree': 9, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 162], [9, 4]], 'label': '486.254', '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': 'C6.C3^4', 'ngens': 6, 'nilpotency_class': 2, 'nilpotent': True, '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': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 166, 'number_divisions': 84, 'number_normal_subgroups': 426, 'number_subgroup_autclasses': 18, 'number_subgroup_classes': 586, 'number_subgroups': 1386, 'old_label': None, 'order': 486, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 1], [3, 242], [6, 242]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 360, 'outer_gen_orders': [2, 9, 2], 'outer_gen_pows': [5471691, 14408200, 27828177], 'outer_gens': [[11225629, 14686477, 25633142, 21546862, 28816400, 10736979], [14686477, 11225629, 38808853, 8405171, 28816400, 24092483], [26473440, 1584140, 25633142, 19702000, 28816400, 42017191]], 'outer_group': '103680.b', 'outer_hash': 1958447605843920035, 'outer_nilpotent': False, 'outer_order': 103680, 'outer_permdeg': 80, 'outer_perms': [12575948016708097444481404785089505670346388640152523348645545429891949901530017632622879304862374720969475581273786959, 43543557791070976013703789721302098172809787794961066842790827369777398562616400994490660163216448528413707164230815862, 5507821184636015958463962700016985234582354617169012910466600165858519404701230307056463378718169076206299392225964625], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GSp(4,3)', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3, 3, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 80], [18, 2]], 'representations': {'PC': {'code': 15422938253898039, 'gens': [1, 2, 3, 5, 6], 'pres': [6, -3, -3, -2, -3, -3, -3, 5996, 50, 4323, 3790]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 2939606, 1017496, 25633100, 28816400, 13886268]}, 'Perm': {'d': 29, 'gens': [304888344611713860501504000000, 5033428764097673289461789253, 7550102686338507196661760000, 2516538717432998222691201987, 2516538717432286673398548480, 806634631153204606767248884]}}, 'schur_multiplier': [3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 6], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6.C_3^4', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '324.159', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 360, 'aut_gen_orders': [24, 10, 12], 'aut_gens': [[1, 3, 9, 27, 81], [374, 34, 18, 337, 647], [324, 360, 9, 4, 118], [1, 339, 9, 687, 571]], 'aut_group': None, 'aut_hash': 3259962041708334845, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 16796160, 'aut_permdeg': 242, 'aut_perms': [179136095562392760086876564263786722413209800315569584938173806406491866762405091081401549364448205431515272671025340784346023835717205751671562607212072732506712318827781583061346210096865702935353762809634700286275061266747650319517047183279560247711246332242331002266037615357820288150542407049292252492680932078516847505730820952904719386548439291793934998420859158641669571843396920592700618856142536284099976477854481038756145914840627636765745668860316144973297140613, 26433166910495069213488037778991951983746215688775043823071410124976536440394337243723352085609310361503652410022239905747272324316565186920627408195366968693659854606068568452739071693259469019597009150741360090540386800967186995595208506536724751927567919675900420665320959466288581924101297479798998235418640755775526387924568318141310855175560137434661257975703375293214270107426659340341821948307353981868145832382384422943465318302182068092100938391818045185186213067, 10086955093289784010402849632089253188762418274579426097251226278297730276756233913230945051499698114357721675903950718174379194883704287744096784463002600233377550073098595271674257611356434022378601618562449602228801370722420076299231063508433200975787103408060663960518720182383233155268432943972204918990069278188408366905727097922765644143742655121136590532486582678152410286147822296998676616156949475384346780189920694798481936169483510603468403220630616203819722520], 'aut_phi_ratio': 51840.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 80, 1], [4, 1, 2, 1], [6, 1, 2, 1], [6, 3, 80, 1], [12, 1, 4, 1], [12, 3, 160, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_3:(C_3^3:C_2).\\SU(4,2).C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '162.55', 'autcent_hash': 55, 'autcent_nilpotent': True, 'autcent_order': 162, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_3^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 360, 'autcentquo_group': '103680.b', 'autcentquo_hash': 1958447605843920035, 'autcentquo_nilpotent': False, 'autcentquo_order': 103680, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\GSp(4,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 1, 2], [3, 3, 80], [4, 1, 2], [6, 1, 2], [6, 3, 80], [12, 1, 4], [12, 3, 160]], 'center_label': '12.2', 'center_order': 12, 'central_product': True, 'central_quotient': '81.15', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 755, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['243.65', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [3, 3, 2, 40], [4, 1, 2, 1], [6, 1, 2, 1], [6, 3, 2, 40], [12, 1, 4, 1], [12, 3, 4, 40]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 28080, 'exponent': 12, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 4]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '162.55', 'hash': 755, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 3, 'inner_gen_orders': [3, 3, 1, 3, 3], 'inner_gens': [[1, 3, 9, 45, 81], [1, 3, 9, 27, 90], [1, 3, 9, 27, 81], [10, 3, 9, 27, 81], [1, 21, 9, 27, 81]], 'inner_hash': 15, 'inner_nilpotent': True, 'inner_order': 81, 'inner_split': True, 'inner_tex': 'C_3^4', 'inner_used': [1, 2, 4, 5], 'irrC_degree': 9, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 18, 'irrep_stats': [[1, 324], [9, 8]], 'label': '972.755', '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': 'C12.C3^4', 'ngens': 7, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 9, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 332, 'number_divisions': 126, 'number_normal_subgroups': 639, 'number_subgroup_autclasses': 27, 'number_subgroup_classes': 879, 'number_subgroups': 2079, 'old_label': None, 'order': 972, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 1], [3, 242], [4, 2], [6, 242], [12, 484]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 360, 'outer_gen_orders': [6, 20, 4], 'outer_gen_pows': [0, 0, 330], 'outer_gens': [[676, 7, 9, 381, 118], [664, 40, 18, 667, 777], [38, 371, 9, 367, 935]], 'outer_group': None, 'outer_hash': 5813020212475488689, 'outer_nilpotent': False, 'outer_order': 207360, 'outer_permdeg': 82, 'outer_perms': [428829472636839693255587422258232255002642198852539994613156213744311631787652942949496380149486089420477226718706234472374, 58992070861421778938036048148960121818495671526406730855940595472073426614794368603688716953845499290036445092473167241840, 111023656928061702099283974948354222655266845632891097180280191134028876327434341953128048954411636039538018653254377215], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times C_2.\\SU(4,2).C_2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 31, 'pgroup': 0, 'primary_abelian_invariants': [4, 3, 3, 3, 3], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 81], [4, 40], [18, 2], [36, 1]], 'representations': {'PC': {'code': 537708410633824264628770937, 'gens': [1, 2, 3, 4, 5], 'pres': [7, 3, 3, 3, 3, 2, 2, 3, 1263, 1061, 102, 2532, 124, 5452]}, 'Perm': {'d': 31, 'gens': [813442103424052579818012672000000, 5033428764097673289461789253, 7550102686338507196661760000, 2516538717432998222691201987, 2516538717432286673398548480, 265557748156802772496809984000000, 806634631153204606767248884]}}, 'schur_multiplier': [3, 3, 3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 3, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.C_3^4', 'transitive_degree': 108, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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}
