-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '486.254', 'ambient_counter': 254, 'ambient_order': 486, 'ambient_tex': 'C_6.C_3^4', 'central': False, 'central_factor': False, 'centralizer_order': 162, 'characteristic': False, 'core_order': 9, 'counter': 11, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '486.254.54.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '54.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '54.15', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 15, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 54, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3^2\\times C_6', 'simple': False, 'solvable': True, 'special_labels': ['C4'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '9.2', 'subgroup_hash': 2, 'subgroup_order': 9, 'subgroup_tex': 'C_3^2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '486.254', 'aut_centralizer_order': 17496, 'aut_label': '54.a1', 'aut_quo_index': 13, 'aut_stab_index': 40, 'aut_weyl_group': '12.4', 'aut_weyl_index': 699840, 'centralizer': '3.a1', 'complements': [], 'conjugacy_class_count': 40, 'contained_in': ['18.a1', '18.a2', '27.a1'], 'contains': ['162.a1', '162.b1'], 'core': '54.a1', 'coset_action_label': None, 'count': 40, 'diagramx': [3960, 3573, 4867, 4981], 'generators': [11495158, 11225629], 'label': '486.254.54.a1', 'mobius_quo': 0, 'mobius_sub': 27, 'normal_closure': '54.a1', 'normal_contained_in': ['18.a1', '18.a2', '27.a1'], 'normal_contains': ['162.a1'], 'normalizer': '1.a1', 'old_label': '54.a1', 'projective_image': '162.55', 'quotient_action_image': '3.1', 'quotient_action_kernel': '18.5', 'quotient_action_kernel_order': 18, 'quotient_fusion': None, 'short_label': '54.a1', 'subgroup_fusion': None, 'weyl_group': '3.1'}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '9.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 3], [1, 7], [4, 3]], 'aut_group': '48.29', 'aut_hash': 29, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 48, 'aut_permdeg': 8, 'aut_perms': [31834, 28334], 'aut_phi_ratio': 8.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 8, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(2,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '48.29', 'autcent_hash': 29, 'autcent_nilpotent': False, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(2,3)', '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], [3, 1, 8]], 'center_label': '9.2', 'center_order': 9, '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': ['3.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['3.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 4]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '9.2', 'hash': 2, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 3], [1, 3]], '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, 9]], 'label': '9.2', 'linC_count': 24, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 6, 'linQ_dim': 4, 'linQ_dim_count': 6, 'linR_count': 6, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 9, 'number_divisions': 5, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 6, 'number_subgroups': 6, 'old_label': None, 'order': 9, 'order_factorization_type': 2, 'order_stats': [[1, 1], [3, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 7], [4, 3]], 'outer_group': '48.29', 'outer_hash': 29, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 8, 'outer_perms': [31834, 28334], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\GL(2,3)', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 6, 'pgroup': 3, 'primary_abelian_invariants': [3, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -3, 3]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16858733, 35931237]}, 'GLFp': {'d': 2, 'p': 7, 'gens': [687, 1374]}, 'Perm': {'d': 6, 'gens': [240, 4]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2', 'transitive_degree': 9, 'wreath_data': None, 'wreath_product': False}
-
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': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '54.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 312, 'aut_gen_orders': [2, 13], 'aut_gens': [[1, 3, 9], [36, 22, 28], [44, 7, 50]], 'aut_group': '11232.a', 'aut_hash': 778507202365856770, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11232, 'aut_permdeg': 15, 'aut_perms': [965974769425, 438185353320], 'aut_phi_ratio': 624.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 26, 1], [6, 1, 26, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(3,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 312, 'autcent_group': '11232.a', 'autcent_hash': 778507202365856770, 'autcent_nilpotent': False, 'autcent_order': 11232, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(3,3)', '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], [3, 1, 26], [6, 1, 26]], 'center_label': '54.15', 'center_order': 54, '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', '3.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 15, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 3]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 13], [6, 1, 2, 13]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 7, 'exponent': 6, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '54.15', 'hash': 15, 'hyperelementary': 3, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 3, 9], [1, 3, 9], [1, 3, 9]], '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, 54]], 'label': '54.15', 'linC_count': 13104, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 1638, 'linQ_dim': 6, 'linQ_dim_count': 1638, 'linR_count': 1638, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2*C6', 'ngens': 4, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 54, 'number_divisions': 28, 'number_normal_subgroups': 56, 'number_subgroup_autclasses': 8, 'number_subgroup_classes': 56, 'number_subgroups': 56, 'old_label': None, 'order': 54, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 1], [3, 26], [6, 26]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 312, 'outer_gen_orders': [2, 13], 'outer_gen_pows': [0, 0], 'outer_gens': [[36, 22, 28], [44, 7, 50]], 'outer_group': '11232.a', 'outer_hash': 778507202365856770, 'outer_nilpotent': False, 'outer_order': 11232, 'outer_permdeg': 15, 'outer_perms': [965974769425, 438185353320], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(3,3)', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 11, 'pgroup': 0, 'primary_abelian_invariants': [2, 3, 3, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 26]], 'representations': {'PC': {'code': 8269, 'gens': [1, 2, 3], 'pres': [4, -3, -3, -2, -3, 34]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [41624334336939899, 125101750005088939, 24992888769124995]}, 'GLFp': {'d': 3, 'p': 7, 'gens': [10475581, 28836015, 22014775, 23068812]}, 'Perm': {'d': 11, 'gens': [3628800, 80640, 240, 4]}}, 'schur_multiplier': [3, 3, 3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [3, 3, 6], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2\\times C_6', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}