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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1728.1701', 'ambient_counter': 1701, 'ambient_order': 1728, 'ambient_tex': 'C_{12}^2.D_6', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 864, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.1701.2.b1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.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': ['C1'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '864.338', 'subgroup_hash': 338, 'subgroup_order': 864, 'subgroup_tex': 'C_{12}^2.C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.1701', 'aut_centralizer_order': None, 'aut_label': '2.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '4.d1.a1', '6.c1.a1', '6.e1.a1'], 'core': '2.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [3, 864, 72, 1296, 6, 576, 48, 76], 'label': '1728.1701.2.b1.a1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '2.b1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1', '6.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.a1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.b1.a1', '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': '48.23', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 6, 6, 6, 12, 6], 'aut_gens': [[1, 24, 72], [323, 336, 516], [821, 312, 372], [485, 48, 72], [343, 312, 84], [689, 48, 504], [223, 312, 84], [131, 48, 504]], 'aut_group': None, 'aut_hash': 862488464858774679, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6912, 'aut_permdeg': 150, 'aut_perms': [42199274588486306518792296879695674308570226260482881523599094085422477113882745808645283400695964133147491479569382480365672279090583095598200653232660298303586757759351839697783828235386744486605824333196166761228717404887926751818313841996619766706485154698930, 30972755885778791033715299264931272241768052334125806976012022327723306171261468183790313768589135515765341340179065215281692621876322554569367846246590955708685302313725302306100109105332627566430785654936062170481630952569335187484745480652871903784880216896125, 32636382278240432647938455010741764096586315071739392611267423416777023808357689154836030961096697513543241329464455441898816670672074384932283743847524899065016039320614982869302138641599255087308709861903529414697244623474764319530051722185727291343218832419048, 10319978551860408290478259419520312419897597505145753247461779371365321462873675987853802388151286624207606677533338845782931621764462773812164866012424027548545174906070515000762537594729468522919768109913247877743029191066104470361717616489673147653434330157522, 21451347075836615835909927904080632782523176995499128907845476195043412162585495841649895604965528030795350840842205687647138975997034168714944212405420212080818502105551541647992303225393255145497561754329477942636432165568108465945118681861781507243261656799773, 33408496275033674417771704584157218218599227216589547073031188057904876437554208034628317338390925898869194737881312996695221772206719350936763288556349693617211469763371959931979428633768508112513005046325610130633576916094141926308339414413461845218472001354152, 40551335254690717393889614378812444182826047748729454303772573301310071125275372114885016493018434364932302224809475727067500550906515789914829601046111951438730152265481929089155515554043173996988559642801400565020237218367432157534928610571496128123897891008723], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [3, 3, 2, 1], [3, 6, 1, 1], [3, 6, 2, 1], [4, 1, 2, 2], [4, 2, 2, 2], [6, 2, 1, 3], [6, 3, 2, 3], [6, 6, 1, 3], [6, 6, 2, 3], [8, 18, 8, 1], [12, 2, 2, 2], [12, 2, 4, 2], [12, 3, 4, 2], [12, 6, 2, 2], [12, 6, 4, 6], [12, 6, 8, 2], [24, 18, 16, 1]], 'aut_supersolvable': True, 'aut_tex': '\\He_3.C_2^6.C_2^2', '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': 6, 'autcentquo_group': '216.102', 'autcentquo_hash': 102, 'autcentquo_nilpotent': False, 'autcentquo_order': 216, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_6.S_3^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [3, 3, 2], [3, 6, 3], [4, 1, 4], [4, 2, 4], [6, 2, 3], [6, 3, 6], [6, 6, 9], [8, 18, 8], [12, 2, 12], [12, 3, 8], [12, 6, 44], [24, 18, 16]], 'center_label': '8.2', 'center_order': 8, 'central_product': False, 'central_quotient': '108.25', 'commutator_count': 1, 'commutator_label': '18.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 338, '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], [3, 3, 2, 1], [3, 6, 1, 1], [3, 6, 2, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [6, 2, 1, 3], [6, 3, 2, 3], [6, 6, 1, 3], [6, 6, 2, 3], [8, 18, 4, 2], [12, 2, 2, 4], [12, 2, 4, 1], [12, 3, 4, 2], [12, 6, 2, 6], [12, 6, 4, 8], [24, 18, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '24.9', 'frattini_quotient': '36.12', 'hash': 338, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 3, 6], 'inner_gens': [[1, 624, 792], [337, 24, 72], [145, 24, 72]], 'inner_hash': 25, 'inner_nilpotent': False, 'inner_order': 108, 'inner_split': True, 'inner_tex': 'C_3^2:D_6', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 48], [2, 60], [6, 16]], 'label': '864.338', 'linC_count': 192, 'linC_degree': 7, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 40, 'linQ_dim': 12, 'linQ_dim_count': 10, 'linR_count': 24, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12^2.C6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 57, 'number_conjugacy_classes': 124, 'number_divisions': 50, 'number_normal_subgroups': 71, 'number_subgroup_autclasses': 138, 'number_subgroup_classes': 163, 'number_subgroups': 530, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 12], [6, 78], [8, 144], [12, 312], [24, 288]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [0, 2, 0, 0, 2], 'outer_gens': [[437, 336, 72], [451, 312, 72], [17, 312, 360], [1, 24, 84], [229, 600, 84]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [120, 1174320, 367920, 368041, 806422], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [2, 8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 12], [4, 15], [6, 4], [8, 10], [12, 4], [24, 1]], 'representations': {'PC': {'code': 3525517001712882145634284697956937868137752345, 'gens': [1, 5, 6], 'pres': [8, -2, -2, -2, -3, -3, -2, -2, -3, 16, 41, 66, 24964, 12012, 3140, 3028, 38021, 141, 40326, 166, 36871]}, 'Perm': {'d': 21, 'gens': [262539173781931263, 80208796, 372491224308403200, 18550, 127370880, 12316, 2689063734976819200, 5251452972974208000]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 24], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}^2.C_6', 'transitive_degree': 288, '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': '24.9', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 6, 12, 12, 6, 12, 6, 12], 'aut_gens': [[1, 12, 144], [1013, 12, 1632], [439, 948, 1080], [1469, 1362, 1032], [799, 516, 144], [1229, 444, 1656], [1561, 1362, 1704], [793, 522, 168], [131, 18, 840], [1609, 1386, 264]], 'aut_group': '6912.or', 'aut_hash': 3679239282322530397, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 27648, 'aut_permdeg': 166, 'aut_perms': [8178622971132521215916779224298625833695923556525802854006405941802376364904991978273771531929706225386828666868895188312062352684644189063876641457906060692568333787589700588591113671564598746590324044383237066381617934852127328882700616816481794111239346125716461307960960734686831398980710231506, 8596381520804540782478061586421259229032098778613349930522578854504633322892099361225042906829731438590657480452195369389039867474631947908556145315555509868427009633958302923821225868641452984635009566164770780948983426993588697168571951581652432310251867836276146998038553430181836886016758147835, 195157570386409128671283088606895555746253183861183097035877589537420195420634806647717812354517496347826346701198439722908603486508713775951214958061798101190131221875503855599458251264084894927241369574079618269833489817227167778878618995361589820191164507390691009382788094783005812424546517551, 2114017181379491139557772368961256450063963269360639211580486886864518574855142872035762962982471108303663397393321611273337005175988627360940815501613846231091744892961354682509541957537631249100218798654807770681405227180062326751490292184774209302641208469076799729743427607070381150192511865587, 4510868310858789811064512416659994532194775874620972469491295152522739595232006160994767571541213005488247853311547485273449659240815615249757649869426814892025626074929896437849312678972434043464799225533717309818611980553148291680060925174637982513073074762267543832635436080851662676674099377661, 7896465346352020891720099089613295105808049452681213763646523236624208080591389909419851242017771708000164935465038148715609499457617226113110356781842030377448046717627781576287367182070111822326859644232084353884002472945118433584292912383151688675448441683317624940625787743589943938080976683797, 548956785249891177061695437208632449045209296909377517740708123141206878111991658579141979431285959050192928754904162267025532042851294629649917776288152750138498709111204445605115267605046236728815283630832780752781396753792191886714135202956388757661258159225733614373649418138112060116682159471, 7390691768106829551212857960985336300888834327161036822221900945894383599766923243391655568800280191972629649662052226795804496323652704739274682408542388661364917734728895579492136747195972939177938122079605435055910204659106969135773792733187089473433303741676845181572651569253455323411833064657, 7623574808314921312839673216322417778567092617053798724294007520085747802453315060980557810104659293651982200426046346019290731802174487953038401452913713031776196001120870542257727102769709937235474316857559386544452794977033120970996405369397636541290664028245450364086886498770703160851704057837], 'aut_phi_ratio': 48.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 2, 1, 1], [3, 3, 2, 1], [3, 6, 1, 1], [3, 6, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 2, 1], [6, 2, 1, 3], [6, 3, 2, 3], [6, 6, 1, 3], [6, 6, 2, 3], [8, 36, 4, 2], [12, 4, 1, 4], [12, 4, 2, 1], [12, 6, 2, 4], [12, 8, 4, 1], [12, 12, 1, 4], [12, 12, 2, 6], [12, 12, 4, 1], [12, 24, 4, 2], [12, 24, 8, 1], [24, 36, 8, 2]], 'aut_supersolvable': True, 'aut_tex': '\\GL(2,3).C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '16.14', 'autcent_hash': 14, 'autcent_nilpotent': True, 'autcent_order': 16, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '1728.46165', 'autcentquo_hash': 46165, 'autcentquo_nilpotent': False, 'autcentquo_order': 1728, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': '\\He_3:C_2^6', 'cc_stats': [[1, 1, 1], [2, 1, 3], [3, 2, 1], [3, 3, 2], [3, 6, 3], [4, 2, 4], [4, 4, 1], [4, 8, 2], [6, 2, 3], [6, 3, 6], [6, 6, 9], [8, 36, 8], [12, 4, 6], [12, 6, 8], [12, 8, 4], [12, 12, 20], [12, 24, 16], [24, 36, 16]], 'center_label': '4.2', 'center_order': 4, 'central_product': False, 'central_quotient': '432.166', 'commutator_count': 2, 'commutator_label': '72.36', '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', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1701, '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], [3, 3, 2, 1], [3, 6, 1, 1], [3, 6, 2, 1], [4, 2, 1, 4], [4, 4, 1, 1], [4, 8, 1, 2], [6, 2, 1, 3], [6, 3, 2, 3], [6, 6, 1, 3], [6, 6, 2, 3], [8, 36, 4, 2], [12, 4, 1, 4], [12, 4, 2, 1], [12, 6, 2, 4], [12, 8, 2, 2], [12, 12, 1, 4], [12, 12, 2, 8], [12, 24, 2, 8], [24, 36, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 24, 'exponent': 24, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '48.20', 'frattini_quotient': '36.12', 'hash': 1701, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [12, 6, 6], 'inner_gens': [[1, 1428, 1704], [457, 12, 1008], [313, 876, 144]], 'inner_hash': 166, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6^2:C_{12}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 54], [4, 21], [6, 8], [12, 6]], 'label': '1728.1701', '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': 'C12^2.D6', 'ngens': 9, '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': 54, 'number_characteristic_subgroups': 76, 'number_conjugacy_classes': 113, 'number_divisions': 62, 'number_normal_subgroups': 86, 'number_subgroup_autclasses': 247, 'number_subgroup_classes': 292, 'number_subgroups': 1323, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 3], [3, 26], [4, 28], [6, 78], [8, 288], [12, 728], [24, 576]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 8, 76, 8, 6, 0], 'outer_gens': [[73, 12, 144], [865, 60, 768], [1, 132, 816], [79, 60, 840], [1, 138, 720], [77, 12, 720]], 'outer_group': '64.267', 'outer_hash': 267, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 12, 'outer_perms': [39916800, 362880, 5040, 120, 6, 1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 25, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 12], [4, 23], [6, 4], [8, 12], [12, 6], [24, 1]], 'representations': {'PC': {'code': 2037184272639607565379469704490646802963741187798995404299460171141584319065734729, 'gens': [1, 4, 7], 'pres': [9, 2, 2, 3, 2, 2, 3, 2, 2, 3, 18, 46, 506, 51411, 1524, 102, 5404, 130, 5189, 107358, 6063, 3804, 5325, 186, 110599, 13840, 6073, 214, 97208, 25289, 13634]}, 'Perm': {'d': 25, 'gens': [700413146587373921868289, 1244429383606103908684800, 16313, 1996429906040255279193600, 2642533253001381003264000, 68349217305600, 3155174664060470059008000, 51932, 98499]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 12], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}^2.D_6', 'transitive_degree': 576, '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}
