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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1632586752.gj', 'ambient_counter': 166, 'ambient_order': 1632586752, 'ambient_tex': 'C_3^{12}.C_2^6.C_6.D_4', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': True, 'core_order': 816293376, 'counter': 8, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '1632586752.gj.2._.G', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.G', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, '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': None, 'standard_generators': False, 'stem': False, 'subgroup': '816293376.wj', 'subgroup_hash': None, 'subgroup_order': 816293376, 'subgroup_tex': 'C_3^6.(C_3^6.C_2^6:S_4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1632586752.gj', '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': [304888344611713860507731020829, 2432922937193553869, 526261673867387060334436198676582640, 319119519553032421315629112783393839680789, 138276935569818277722350190176452642799285, 295241031024924221159929707714161742984, 15511212476232994160645045, 43545600, 8223143542523660965215856398969629, 271353675587871452985655043301504000, 20666567286448296560433475021905592365360, 64119255297506646251104778966520023249307, 9146650390055449292815153113840, 174356627760, 806582922253211271168000000, 51704033477769953280000, 45360, 10628907027099616509281192408069578752004, 20666567286447877757767170889300377600000, 526261673867387060334436024320045360, 304888345735714588279115308824, 20922793521845], 'label': '1632586752.gj.2._.G', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '2.G', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2._.G', 'subgroup_fusion': None, 'weyl_group': None}
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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': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[191470684358043620645364254247713864588426, 137978731856336360191289806866484948888799, 361359785365242501525041777216075903093639], [191765917157083628078797121814948195217444, 137978731856336360191292117788547163551759, 361359785365242501525041777216169344693735], [191470939266042287941222686638202526569005, 148607112630298595155411308566213764511756, 371988437475197188101681598825203400373732], [255290064502007374492189177426605277454668, 148311879831258975504472903173604048833237, 74156067205264272805221395119007356721731], [287502193492722761457796346580026209061067, 74459448324902087258066385709667021982718, 148608461962744616680195659614951869894915], [191470939266042287941222687014812744553002, 148311879831259394280172921447498470775413, 361360056709771439031167328878036680373735], [191470676135510258104638277339461685635989, 138273964663912434715656182079161439642694, 371988174353202000891805090958439261840716], [159563006581713790931012098111818215255756, 106362772414768298477070040921302344936253, 7053576268103145103445981036535507840], [170192202203923609270770605157419594724211, 116400687582115226994436123446061671656254, 7868433053882421842027937636519694200], [159563303399357355380893129680065952168815, 297535779320996288040216163926726090292414, 7605293375589975450941029138714538160], [191470421245194696018316094555935838641445, 116696191717147298336568033553628173504052, 371988174353202807447751326703047845565836], [202099065123469757547833640570689999637149, 137978731856335972384060151243125140760891, 371988437475197188128657616291691628111331], [191470684358043620645364254247807349698602, 148607112621761302703609839613313469685759, 361359785356096238915237411198003835206135], [212137235216498101839739426365515910011641, 148607112621761721454579287329072852294252, 351322141533888024593220308055940495503092], [212137235207960840385632339320307110677146, 148607112621762109234825504799706099014399, 361360056709771439058143346344699184940679], [202099320049151561050920393637461829964186, 148607112621762109234828059012050046278159, 361360056701234565382039340783901083263319], [202099320031467649283189907165274254203641, 148607112621761302651908116681076428056895, 351322141542425286022599379424632207503092], [191470413004368032800887286770801408908426, 127940816688989819427198790149712637848799, 361359530457244221982458410256964038773639], [191470684358043620645364253871103726437881, 137978731856335972411036169044726763417036, 351321870197895960736222744488196179548132], [191470684375727532413094741054840558437881, 137978731856335972411041034848568716568892, 351321870180212436697039307101339037848772], [191470684358043620645364254247713900876186, 137978731856336360191292118123392716696895, 361359785365242501525041777216075939381495], [202099065132615601251563635500710351717881, 137978731856335553608364998773259642271851, 371988166121521600230228613881534955142275], [191470684358044008425615337522363464588282, 137978731856336360191287252319201963289039, 361359785365242501525041777216075939417015], [212136708946286554195905700416912857996425, 148607383966290659039382578678558442831356, 371988437475197994659875836025367199448772], [159559747016906943510546005294291133166229, 148607112630298595155408997644070634831356, 371988437475197188101681598825203400408772], [275955842404785809870515434189570265313400, 138274235999904498572656177816690926950397, 64117888907386089957816047818045699313735]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 6530347008, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 243, 1, 1], [2, 243, 2, 1], [2, 486, 1, 1], [2, 972, 1, 2], [2, 2916, 1, 2], [2, 4374, 4, 2], [2, 5832, 2, 1], [2, 8748, 1, 2], [2, 19683, 1, 1], [2, 19683, 2, 1], [2, 39366, 1, 1], [2, 52488, 2, 1], [2, 78732, 1, 2], [2, 531441, 1, 1], [3, 12, 2, 2], [3, 16, 2, 1], [3, 24, 1, 2], [3, 24, 2, 2], [3, 32, 2, 2], [3, 48, 1, 1], [3, 48, 2, 4], [3, 48, 4, 1], [3, 96, 1, 1], [3, 96, 2, 9], [3, 96, 4, 3], [3, 128, 2, 2], [3, 192, 1, 4], [3, 192, 2, 22], [3, 192, 4, 8], [3, 256, 1, 1], [3, 256, 2, 1], [3, 256, 4, 1], [3, 384, 1, 3], [3, 384, 2, 24], [3, 384, 4, 12], [3, 512, 2, 1], [3, 768, 1, 1], [3, 768, 2, 38], [3, 768, 4, 28], [3, 768, 8, 2], [3, 1536, 2, 24], [3, 1536, 4, 25], [3, 1536, 8, 7], [3, 839808, 1, 1], [4, 52488, 2, 2], [4, 472392, 2, 3], [4, 708588, 2, 2], [4, 944784, 4, 2], [4, 1417176, 1, 2], [4, 4251528, 2, 1], [6, 972, 2, 4], [6, 1944, 2, 16], [6, 1944, 4, 3], [6, 3888, 1, 6], [6, 3888, 2, 26], [6, 3888, 4, 11], [6, 7776, 1, 6], [6, 7776, 2, 34], [6, 7776, 4, 34], [6, 8748, 4, 2], [6, 11664, 2, 3], [6, 15552, 1, 6], [6, 15552, 2, 56], [6, 15552, 4, 42], [6, 17496, 2, 4], [6, 17496, 4, 11], [6, 23328, 2, 9], [6, 31104, 1, 3], [6, 31104, 2, 44], [6, 31104, 4, 32], [6, 34992, 1, 4], [6, 34992, 2, 6], [6, 34992, 4, 16], [6, 46656, 2, 17], [6, 46656, 4, 4], [6, 62208, 2, 23], [6, 62208, 4, 16], [6, 62208, 8, 1], [6, 69984, 1, 6], [6, 69984, 2, 10], [6, 69984, 4, 24], [6, 78732, 2, 2], [6, 93312, 2, 19], [6, 93312, 4, 10], [6, 104976, 2, 1], [6, 139968, 1, 4], [6, 139968, 2, 14], [6, 139968, 4, 14], [6, 157464, 1, 2], [6, 157464, 2, 6], [6, 157464, 4, 2], [6, 186624, 1, 1], [6, 186624, 2, 12], [6, 186624, 4, 13], [6, 186624, 8, 1], [6, 209952, 2, 4], [6, 279936, 1, 6], [6, 279936, 2, 9], [6, 279936, 4, 7], [6, 314928, 1, 1], [6, 314928, 2, 9], [6, 419904, 2, 6], [6, 419904, 4, 1], [6, 559872, 1, 1], [6, 559872, 2, 2], [6, 629856, 1, 1], [6, 629856, 2, 2], [6, 629856, 4, 2], [6, 839808, 2, 4], [6, 839808, 4, 1], [6, 1259712, 1, 2], [6, 1679616, 2, 2], [6, 7558272, 1, 2], [6, 68024448, 1, 1], [9, 1679616, 2, 4], [9, 3359232, 2, 2], [9, 3359232, 4, 3], [12, 104976, 2, 6], [12, 209952, 2, 10], [12, 419904, 2, 16], [12, 419904, 4, 3], [12, 839808, 2, 10], [12, 839808, 4, 3], [12, 944784, 2, 5], [12, 1417176, 4, 2], [12, 1889568, 2, 7], [12, 1889568, 4, 6], [12, 2834352, 2, 4], [12, 3779136, 2, 5], [12, 3779136, 4, 6], [12, 5668704, 1, 2], [12, 7558272, 4, 2], [12, 8503056, 2, 1], [18, 15116544, 2, 4]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 243, 3], [2, 486, 1], [2, 972, 2], [2, 2916, 2], [2, 4374, 8], [2, 5832, 2], [2, 8748, 2], [2, 19683, 3], [2, 39366, 1], [2, 52488, 2], [2, 78732, 2], [2, 531441, 1], [3, 12, 4], [3, 16, 2], [3, 24, 6], [3, 32, 4], [3, 48, 13], [3, 96, 31], [3, 128, 4], [3, 192, 80], [3, 256, 7], [3, 384, 99], [3, 512, 2], [3, 768, 205], [3, 1536, 204], [3, 839808, 1], [4, 52488, 4], [4, 472392, 6], [4, 708588, 4], [4, 944784, 8], [4, 1417176, 2], [4, 4251528, 2], [6, 972, 8], [6, 1944, 44], [6, 3888, 102], [6, 7776, 210], [6, 8748, 8], [6, 11664, 6], [6, 15552, 286], [6, 17496, 52], [6, 23328, 18], [6, 31104, 219], [6, 34992, 80], [6, 46656, 50], [6, 62208, 118], [6, 69984, 122], [6, 78732, 4], [6, 93312, 78], [6, 104976, 2], [6, 139968, 88], [6, 157464, 22], [6, 186624, 85], [6, 209952, 8], [6, 279936, 52], [6, 314928, 19], [6, 419904, 16], [6, 559872, 5], [6, 629856, 13], [6, 839808, 12], [6, 1259712, 2], [6, 1679616, 4], [6, 7558272, 2], [6, 68024448, 1], [9, 1679616, 8], [9, 3359232, 16], [12, 104976, 12], [12, 209952, 20], [12, 419904, 44], [12, 839808, 32], [12, 944784, 10], [12, 1417176, 8], [12, 1889568, 38], [12, 2834352, 8], [12, 3779136, 34], [12, 5668704, 2], [12, 7558272, 8], [12, 8503056, 2], [18, 15116544, 8]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '816293376.wj', 'commutator_count': 1, 'commutator_label': '102036672.gq', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 22, 'conjugacy_classes_known': False, 'counter': 582, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 243, 1, 3], [2, 486, 1, 1], [2, 972, 1, 2], [2, 2916, 1, 2], [2, 4374, 1, 8], [2, 5832, 1, 2], [2, 8748, 1, 2], [2, 19683, 1, 3], [2, 39366, 1, 1], [2, 52488, 1, 2], [2, 78732, 1, 2], [2, 531441, 1, 1], [3, 12, 1, 4], [3, 16, 1, 2], [3, 24, 1, 6], [3, 32, 1, 4], [3, 48, 1, 13], [3, 96, 1, 31], [3, 128, 1, 4], [3, 192, 1, 80], [3, 256, 1, 7], [3, 384, 1, 99], [3, 512, 1, 2], [3, 768, 1, 205], [3, 1536, 1, 204], [3, 839808, 1, 1], [4, 52488, 1, 4], [4, 472392, 1, 6], [4, 708588, 1, 4], [4, 944784, 1, 8], [4, 1417176, 1, 2], [4, 4251528, 1, 2], [6, 972, 1, 8], [6, 1944, 1, 44], [6, 3888, 1, 102], [6, 7776, 1, 210], [6, 8748, 1, 8], [6, 11664, 1, 6], [6, 15552, 1, 286], [6, 17496, 1, 52], [6, 23328, 1, 18], [6, 31104, 1, 219], [6, 34992, 1, 80], [6, 46656, 1, 50], [6, 62208, 1, 118], [6, 69984, 1, 122], [6, 78732, 1, 4], [6, 93312, 1, 78], [6, 104976, 1, 2], [6, 139968, 1, 88], [6, 157464, 1, 22], [6, 186624, 1, 85], [6, 209952, 1, 8], [6, 279936, 1, 52], [6, 314928, 1, 19], [6, 419904, 1, 16], [6, 559872, 1, 5], [6, 629856, 1, 13], [6, 839808, 1, 12], [6, 1259712, 1, 2], [6, 1679616, 1, 4], [6, 7558272, 1, 2], [6, 68024448, 1, 1], [9, 1679616, 1, 6], [9, 1679616, 2, 1], [9, 3359232, 1, 8], [9, 3359232, 2, 4], [12, 104976, 1, 12], [12, 209952, 1, 20], [12, 419904, 1, 36], [12, 419904, 2, 4], [12, 839808, 1, 24], [12, 839808, 2, 4], [12, 944784, 1, 10], [12, 1417176, 1, 8], [12, 1889568, 1, 38], [12, 2834352, 1, 8], [12, 3779136, 1, 34], [12, 5668704, 1, 2], [12, 7558272, 1, 8], [12, 8503056, 1, 2], [18, 15116544, 1, 6], [18, 15116544, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 36, 'exponents_of_order': [13, 9], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 32], [48, 1, 152], [96, 1, 344], [128, 0, 4], [128, 1, 10], [192, 0, 8], [192, 1, 520], [256, 0, 4], [256, 1, 18], [384, 0, 8], [384, 1, 420], [512, 0, 4], [512, 1, 8], [768, 1, 410], [1536, 1, 204]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '816293376.wj', 'hash': 1714575866105904601, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_3^6.(C_3^6.C_2^6:S_4)', 'inner_used': None, 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 4], [3, 24], [6, 20], [12, 100], [16, 4], [24, 168], [32, 18], [48, 268], [64, 8], [96, 446], [128, 14], [192, 544], [256, 22], [384, 430], [512, 12], [768, 410], [1536, 204]], 'label': '816293376.wj', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^6.(C3^6.C2^6:S4)', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 4, 0, 0, 0, 0, 9, 0, 0, 0, 4, 0, 0, 3, 0, 1, 1, 7, 0, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1009, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 2704, 'number_divisions': 2690, 'number_normal_subgroups': 52, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 816293376, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 965439], [3, 1371248], [4, 24774336], [6, 217693008], [9, 67184640], [12, 383372352], [18, 120932352]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '8.5', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 8, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': None, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 4], [3, 24], [6, 20], [12, 100], [16, 4], [24, 168], [32, 18], [48, 268], [64, 8], [96, 446], [128, 10], [192, 536], [256, 20], [384, 426], [512, 10], [768, 414], [1024, 2], [1536, 204]], 'representations': {'PC': {'code': '130514296904099625339102605947669284881541021344210961335439922807702001944992641115278799821120865973232985532569533400328411387424275168145270068212309581437118187206065291045951320797688951418476596407228501621014270082999769583061502775556756883627174695775995801810761860734015544437274207878997333049314714036484528519034048635784378122996616252658523299240765525377881941677527935139473290853178875105213858943969687633533914108066452730486799526349192267698745791815695820135567232067447296899423421376341355220044575391239459278584458970832799667556473530093640674003848365919252757242356466273464960445051304086511071320769736039665236019526314915218409276496873441076595576858913141414333506103516966827170058983152554502816159811965527727813167661274366158368658926347054544802654165395129261954811687945517525465456879531767032601633527158698417208206607766668300699888162082089518562177059354776431322178541186003887463493819516246523904616754545250548568181008053138894371696811593984175910290182847645866351744269170383784162048680040407029749180670115598351873187268917445564508530343016292842711059459344024899381797981761554532958321900794831853456678683233631892774655333473918111703657900992693702172311138225934075363316073946488583147711467845629279527070323047316094935368594998899056480538093175073131930117864903278554493995949975348112589235502077363253896916320842421583083507767774937955876550797512114521151876956227561297461682446492017084463061282935455899075500767995401663970042193492942078367231', 'gens': [1, 2, 4, 5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22], 'pres': [22, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4799885112, 12336115881, 111, 26077895450, 32288050083, 21394837225, 11160212759, 1114039237, 16537664884, 6090713666, 1976932698, 608281370, 312, 106026528965, 45250948539, 15076673617, 8598928343, 1500415603, 89573313990, 7325375932, 10840841138, 8555164536, 5062878838, 2438652024, 446, 21931015, 68134606877, 13474450227, 5702535241, 4039495775, 2245682677, 74533692032, 63171152778, 39510344266, 9315505658, 5101168344, 1916246494, 304167344, 432855684, 580, 170126246409, 81088254751, 2771493173, 12566829515, 6843388737, 666621239, 335874141, 126393425938, 54589785524, 15156300576, 3372211996, 6704705930, 1715236104, 1075139350, 5493080, 300989622, 103865398, 714, 130496762891, 90650875425, 18771401143, 7417681997, 6419990115, 2308635769, 6523, 3420945540, 91339012942, 50300715950, 11019486270, 8548710556, 1333002650, 1081265472, 1070300254, 74244644, 184653822, 57412444, 15913580, 848, 121781366797, 54020736035, 42704604153, 10043066959, 5023130213, 1760597115, 880298641, 182464317, 3130745, 148599982094, 28596395556, 33123055738, 14997312080, 3773278182, 423189550, 36709434, 4238, 263219202063, 94552584229, 38681634875, 15654279249, 4023714919, 1063839869, 2717992083, 39802987, 9846423, 146326321168, 134290151462, 16960977852, 8525620306, 11728544360, 1150687422, 575343796, 242588, 10448344, 191244810257, 110559043623, 4594537789, 11260643411, 9577294953, 6149354239, 3074677205, 510307969, 85037277, 128585, 317444100882, 109264611496, 72496448702, 13855716948, 6656272234, 3147439808, 3198362262, 67806482, 88151422, 12745938, 146018104339, 37499235881, 27371520063, 6493639765, 1629619307, 7327584129, 508654231, 523860675, 8585519, 12854443, 283262474900, 88634988330, 77124180736, 25962152918, 14787710892, 1621420546, 3681726200, 292789924, 87068760, 5605268, 139503513621, 150483142699, 35558620481, 26810099799, 304432237, 6953848835, 3476924505, 459157445, 76212817, 793077]}, 'Perm': {'d': 36, 'gens': [191470684358043620645364254247713864588426, 137978731856336360191289806866484948888799, 361359785365242501525041777216075903093639]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 18, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^6.(C_3^6.C_2^6:S_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[319414497444378634338309251967344033927160, 319119519553032421315629112783393839680789, 159858536061040581529426799878260320765255], [319414497444378215508664376197577823899064, 319119790906707590384410927790440680750245, 169896977490061377485562116120736904940611], [329452938891081759891772063996000370800584, 329748171689817282245075771583222751892405, 96035048055929033553769492892883690055824], [127942972700235056304267317083659255105357, 137980624719366043267900969489490651174395, 297535779449817936575525043150501607501172], [340080793385687379044096817917937674458923, 319119519562178652903013392139587265172405, 180229590981081666698678208266603746683359], [212433019760113647633280241435328978545132, 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None, 'aut_stats': [[1, 1, 1, 1], [2, 243, 1, 1], [2, 486, 1, 2], [2, 972, 1, 2], [2, 2916, 1, 2], [2, 5832, 2, 1], [2, 8748, 1, 2], [2, 8748, 2, 2], [2, 11664, 1, 1], [2, 17496, 2, 1], [2, 19683, 1, 1], [2, 39366, 1, 2], [2, 78732, 1, 2], [2, 104976, 1, 1], [2, 531441, 1, 1], [3, 24, 1, 4], [3, 32, 1, 1], [3, 48, 1, 3], [3, 64, 1, 2], [3, 96, 1, 5], [3, 96, 2, 1], [3, 128, 2, 2], [3, 192, 1, 13], [3, 192, 2, 3], [3, 256, 1, 1], [3, 384, 1, 25], [3, 384, 2, 12], [3, 512, 1, 1], [3, 512, 2, 1], [3, 768, 1, 21], [3, 768, 2, 16], [3, 1024, 1, 1], [3, 1536, 1, 34], [3, 1536, 2, 30], [3, 1536, 4, 3], [3, 3072, 1, 22], [3, 3072, 2, 24], [3, 3072, 4, 7], [3, 839808, 1, 1], [4, 104976, 1, 2], [4, 708588, 2, 2], [4, 944784, 1, 3], [4, 1417176, 1, 2], [4, 1417176, 2, 2], [4, 1417176, 4, 1], [4, 1889568, 2, 4], [4, 8503056, 1, 1], [6, 1944, 1, 4], [6, 3888, 1, 22], [6, 3888, 2, 7], [6, 7776, 1, 28], [6, 7776, 2, 11], [6, 15552, 1, 40], [6, 15552, 2, 38], [6, 17496, 2, 2], [6, 23328, 1, 3], [6, 31104, 1, 55], [6, 31104, 2, 50], [6, 31104, 4, 1], [6, 34992, 1, 8], [6, 34992, 2, 11], [6, 46656, 1, 9], [6, 62208, 1, 36], [6, 62208, 2, 35], [6, 69984, 1, 12], [6, 69984, 2, 20], [6, 69984, 4, 2], [6, 93312, 1, 17], [6, 93312, 2, 6], [6, 124416, 1, 19], [6, 124416, 2, 16], [6, 124416, 4, 1], [6, 139968, 1, 14], [6, 139968, 2, 28], [6, 139968, 4, 2], [6, 157464, 1, 4], [6, 186624, 1, 19], [6, 186624, 2, 12], [6, 209952, 1, 1], [6, 279936, 1, 20], [6, 279936, 2, 20], [6, 279936, 4, 6], [6, 314928, 1, 7], [6, 314928, 2, 4], [6, 373248, 1, 12], [6, 373248, 2, 13], [6, 373248, 4, 1], [6, 419904, 1, 4], [6, 559872, 1, 9], [6, 559872, 2, 13], [6, 559872, 4, 2], [6, 629856, 1, 8], [6, 839808, 1, 6], [6, 839808, 2, 1], [6, 1119744, 1, 2], [6, 1119744, 2, 2], [6, 1119744, 4, 1], [6, 1259712, 1, 4], [6, 1259712, 2, 2], [6, 1679616, 1, 4], [6, 1679616, 2, 1], [6, 3359232, 1, 2], [6, 7558272, 1, 2], [6, 7558272, 4, 1], [6, 68024448, 1, 1], [8, 17006112, 4, 1], [9, 1679616, 2, 2], [9, 3359232, 1, 2], [9, 3359232, 4, 1], [9, 6718464, 1, 2], [9, 6718464, 2, 2], [12, 209952, 1, 6], [12, 419904, 1, 10], [12, 839808, 1, 16], [12, 839808, 2, 3], [12, 1679616, 1, 10], [12, 1679616, 2, 3], [12, 1889568, 1, 5], [12, 2834352, 2, 4], [12, 3779136, 1, 7], [12, 3779136, 2, 8], [12, 3779136, 4, 2], [12, 5668704, 1, 4], [12, 5668704, 2, 4], [12, 5668704, 4, 2], [12, 7558272, 1, 5], [12, 7558272, 2, 8], [12, 7558272, 4, 2], [12, 15116544, 2, 4], [12, 17006112, 1, 1], [18, 15116544, 2, 2], [18, 15116544, 4, 2], [18, 30233088, 1, 2], [18, 30233088, 4, 1], [24, 34012224, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 243, 1], [2, 486, 2], [2, 972, 2], [2, 2916, 2], [2, 5832, 2], [2, 8748, 6], [2, 11664, 1], [2, 17496, 2], [2, 19683, 1], [2, 39366, 2], [2, 78732, 2], [2, 104976, 1], [2, 531441, 1], [3, 24, 4], [3, 32, 1], [3, 48, 3], [3, 64, 2], [3, 96, 7], [3, 128, 4], [3, 192, 19], [3, 256, 1], [3, 384, 49], [3, 512, 3], [3, 768, 53], [3, 1024, 1], [3, 1536, 106], [3, 3072, 98], [3, 839808, 1], [4, 104976, 2], [4, 708588, 4], [4, 944784, 3], [4, 1417176, 10], [4, 1889568, 8], [4, 8503056, 1], [6, 1944, 4], [6, 3888, 36], [6, 7776, 50], [6, 15552, 116], [6, 17496, 4], [6, 23328, 3], [6, 31104, 159], [6, 34992, 30], [6, 46656, 9], [6, 62208, 106], [6, 69984, 60], [6, 93312, 29], [6, 124416, 55], [6, 139968, 78], [6, 157464, 4], [6, 186624, 43], [6, 209952, 1], [6, 279936, 84], [6, 314928, 15], [6, 373248, 42], [6, 419904, 4], [6, 559872, 43], [6, 629856, 8], [6, 839808, 8], [6, 1119744, 10], [6, 1259712, 8], [6, 1679616, 6], [6, 3359232, 2], [6, 7558272, 6], [6, 68024448, 1], [8, 17006112, 4], [9, 1679616, 4], [9, 3359232, 6], [9, 6718464, 6], [12, 209952, 6], [12, 419904, 10], [12, 839808, 22], [12, 1679616, 16], [12, 1889568, 5], [12, 2834352, 8], [12, 3779136, 31], [12, 5668704, 20], [12, 7558272, 29], [12, 15116544, 8], [12, 17006112, 1], [18, 15116544, 12], [18, 30233088, 6], [24, 34012224, 4]], 'center_label': '1.1', 'center_order': None, 'central_product': None, 'central_quotient': '1632586752.gj', 'commutator_count': None, 'commutator_label': '204073344.dj', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 23, 'conjugacy_classes_known': False, 'counter': 166, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 243, 1, 1], [2, 486, 1, 2], [2, 972, 1, 2], [2, 2916, 1, 2], [2, 5832, 1, 2], [2, 8748, 1, 6], [2, 11664, 1, 1], [2, 17496, 1, 2], [2, 19683, 1, 1], [2, 39366, 1, 2], [2, 78732, 1, 2], [2, 104976, 1, 1], [2, 531441, 1, 1], [3, 24, 1, 4], [3, 32, 1, 1], [3, 48, 1, 3], [3, 64, 1, 2], [3, 96, 1, 7], [3, 128, 1, 4], [3, 192, 1, 19], [3, 256, 1, 1], [3, 384, 1, 49], [3, 512, 1, 3], [3, 768, 1, 53], [3, 1024, 1, 1], [3, 1536, 1, 106], [3, 3072, 1, 98], [3, 839808, 1, 1], [4, 104976, 1, 2], [4, 708588, 1, 4], [4, 944784, 1, 3], [4, 1417176, 1, 10], [4, 1889568, 1, 8], [4, 8503056, 1, 1], [6, 1944, 1, 4], [6, 3888, 1, 36], [6, 7776, 1, 50], [6, 15552, 1, 116], [6, 17496, 1, 4], [6, 23328, 1, 3], [6, 31104, 1, 159], [6, 34992, 1, 30], [6, 46656, 1, 9], [6, 62208, 1, 106], [6, 69984, 1, 60], [6, 93312, 1, 29], [6, 124416, 1, 55], [6, 139968, 1, 78], [6, 157464, 1, 4], [6, 186624, 1, 43], [6, 209952, 1, 1], [6, 279936, 1, 84], [6, 314928, 1, 15], [6, 373248, 1, 42], [6, 419904, 1, 4], [6, 559872, 1, 43], [6, 629856, 1, 8], [6, 839808, 1, 8], [6, 1119744, 1, 10], [6, 1259712, 1, 8], [6, 1679616, 1, 6], [6, 3359232, 1, 2], [6, 7558272, 1, 2], [6, 7558272, 2, 2], [6, 68024448, 1, 1], [8, 17006112, 1, 4], [9, 1679616, 1, 2], [9, 1679616, 2, 1], [9, 3359232, 1, 2], [9, 3359232, 2, 2], [9, 6718464, 1, 4], [9, 6718464, 2, 1], [12, 209952, 1, 6], [12, 419904, 1, 10], [12, 839808, 1, 18], [12, 839808, 2, 2], [12, 1679616, 1, 12], [12, 1679616, 2, 2], [12, 1889568, 1, 5], [12, 2834352, 1, 8], [12, 3779136, 1, 23], [12, 3779136, 2, 4], [12, 5668704, 1, 20], [12, 7558272, 1, 21], [12, 7558272, 2, 4], [12, 15116544, 1, 8], [12, 17006112, 1, 1], [18, 15116544, 1, 2], [18, 15116544, 2, 5], [18, 30233088, 1, 2], [18, 30233088, 2, 2], [24, 34012224, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [13, 10], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': None, 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1632586752.gj', 'hash': 8292149545681896644, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_3^{12}.C_2^6.C_6.D_4', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '1632586752.gj', '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': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^12.C2^6.C6.D4', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 10, 0, 0, 0, 0, 10, 0, 0, 0, 6, 0, 1, 3, 0, 3, 1, 7, 0, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 1075, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 1628, 'number_divisions': 1603, 'number_normal_subgroups': 62, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1632586752, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1012095], [3, 1371248], [4, 43670016], [6, 281891664], [8, 68024448], [9, 67184640], [12, 670586688], [18, 362797056], [24, 136048896]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '4.2', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 4, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '928792784323921272324242691906032081971166295765701305092752441274140316938104779926011201394595202817747021633141067010904441135861346235679266501772880809402011046276717937252431649930820860504644860473101094790553627394834534562108919610724532225020945244990509771550542094114254652723457251101215359792923967047234072582627646942032532420614934524093877333568656138790560012589291527995984941152941730078693668001427145046808499380636551106637717630824003929675522090103099737812864809063557299583197393483473569703650288811084614628169250042580195699272928914029473009637761968972401659213618139435428101097921892030283696027779487244557183567328539914961350389560409910877172682525302316082889781929139683688589675808847026467419129058919574028369400026824475610528398137445232233796042346110762161766915725446941284451867116753272062252272603744317613938482769955673565269963987723851093975634314536212953801428030700138508539985378890843736848717565602195274418439308904881610859655258566629573880462736246965865438591956724446144754506405985876202931417391050257181650486992483812343221032527759230574582954973472313197564816421447214235444804603057872162351878170509515484761060070810993121949928933798500597230726797582693716462407834149080581914820613564268929149985404834620370081954593268510921674358533949153325667322845966276427997682013327905713722717130819240912324814293425697581651703521947423690719262294628564637075404172611243664434758538109281163506101219424934939222651331658422995323849322511687896199193954488782552962272659323800464264329047980305737385544413326566021474477767328632075620088395849345036750733119139528846989926881041623807', 'gens': [1, 2, 4, 5, 7, 9, 11, 13, 15, 17, 18, 19, 20, 21, 22, 23], 'pres': [23, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 16643837760, 32109198761, 116, 28369294250, 6460234896, 141065922819, 6630253082, 26660771221, 132611852794, 56423772297, 19358781500, 5244763, 326, 69914100965, 961606108, 15428251563, 12447823634, 341261976, 33260338278, 102875875019, 52558298551, 1512345203, 8546943342, 398302851, 466, 72891167239, 98277691422, 59074209845, 125914956, 10305904867, 28090, 318907644488, 33686701447, 67926840570, 1356396557, 10978471972, 3964387119, 2775126188, 1074705874, 606, 227897174409, 114639183392, 6825237175, 27666887758, 13833443941, 11164, 264794603974, 78020579241, 34302133724, 22391180143, 11343285462, 4946318117, 3798373144, 1324344357, 103838984, 746, 293322166283, 1133180962, 73330541625, 318032, 1364968039, 6819, 96002426064, 57641085485, 86814459595, 11083066592, 8502483727, 4337267838, 1565161121, 73033936, 5477324, 886, 38219102221, 1112868, 661022267, 13374015081, 556544, 278359, 46565, 7971, 166765728794, 102119053357, 36631158900, 2092521683, 16570863466, 106414689, 476182952, 14978695, 1714158, 44327224, 22805480, 1026, 129393745935, 91066540070, 92326495549, 4235120724, 14312927339, 3815554, 277572249, 318151, 53237, 18856611, 14253470247, 44876540222, 48646741, 231071724, 12161795, 169158, 28444, 5030, 57277145105, 208043425768, 4292415, 7919389549, 19315739, 3219465, 536791, 89717, 15243, 631130754450, 203941089833, 50400797248, 271849047, 271849070, 122332165, 1699304, 283470, 47536, 713487644179, 165455861802, 15996430145, 4111119448, 27787680111, 944317574, 512697757, 43519883, 13115769, 23129095, 105221, 330871754324, 50720425099, 55260733314, 651006809, 21905541616, 1261951623, 98903102, 107666700, 16901386, 23346584, 301734, 582629967765, 297712394540, 174898228099, 9107417178, 11883827057, 3281503240, 1163346783, 325920877, 70496171, 38460345, 2143759, 9082819990, 389501345805, 119194923332, 70872931675, 29183939826, 17054587721, 3761113984, 1011922190, 166597164, 17070070, 3847232]}, 'Perm': {'d': 36, 'gens': [319414497444378634338309251967344033927160, 159858536061040581529426799878260320765255, 319119519553032421315629112783393839680789]}}, 'schur_multiplier': None, 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 18, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^{12}.C_2^6.C_6.D_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
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}
