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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5184.ff', 'ambient_counter': 136, 'ambient_order': 5184, 'ambient_tex': 'C_3^4:C_4^2:C_2^2', 'central': True, 'central_factor': False, 'centralizer_order': 5184, 'characteristic': True, 'core_order': 2, 'counter': 336, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5184.ff.2592.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '2592.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2592.ci', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 1359974926057248800, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 2592, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3:S_3^3:C_2^2', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'Phi', 'U0', 'Z', 'Phi', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5184.ff', 'aut_centralizer_order': None, 'aut_label': '2592.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['864.a1', '864.b1', '864.c1', '1296.a1', '1296.b1', '1296.c1', '1296.d1'], 'contains': ['5184.a1'], 'core': '2592.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5909, 9638, 5775, 8123], 'generators': [7], 'label': '5184.ff.2592.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '2592.a1', 'normal_contained_in': ['32.a1'], 'normal_contains': ['5184.a1'], 'normalizer': '1.a1', 'old_label': '2592.a1', 'projective_image': '2592.ci', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2592.ci', 'quotient_action_kernel_order': 2592, 'quotient_fusion': None, 'short_label': '2592.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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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}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '32.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [24, 4, 4, 8, 4], 'aut_gens': [[2879290997287, 4035153024017, 1328391555240, 204387127], [9440766281640, 2966618069302, 15284078587567, 10862374523040], [2879290997287, 3314872930457, 9434463056040, 1322052041647], [8563293098760, 203747177, 1323968220840, 15689520], [37896364800, 878736510142, 15284078587560, 10917090254887], [14665160700840, 7206699993257, 1328391555240, 5699647312687]], 'aut_group': None, 'aut_hash': 6148241670926445892, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 144, 'aut_perms': [2956370211950635059086805705137391656757300763195586977198823272888985897601914967359841956494435108397700211590077637496610145435673829767681749413188426992746850395234884366771617721703128917382440716866780342842452019707591804385738919729239879326, 2172174657951613796249203941242676947745406030907635778317887403392707056235357213254336652841747817140898106494368283903103339987828079900650943243696445740077463693699891302461037450595510417930686727986265517720204046552776644940002226285849479475, 4064389229724298502835627306819678504223313255729803351187452133646174811703769007907899448055603710726263437258446159501424683729113444028984583006992031629643333280760523960817262273849347001132419757755503682128248354753738824563801368159335512058, 511336471060292743007116183652805229464609714840378578675611089072825331837320926286394441196471870183757162024296319920339728614020162123891585347046608960320900197552871773419899205176515218130217845568875169445721092731829978205509274822557043103, 2909934532499644610522591420421869937144971129713225927880707014702055129398802079256815324904388313540372223268888788203112837514783077016952968604218303366470283418681669966165148079992261472159852095839355475121395192822493179880176622583926849009], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 2, 1], [2, 18, 8, 1], [2, 81, 1, 2], [3, 8, 2, 1], [3, 8, 4, 1], [3, 32, 1, 1], [4, 18, 8, 1], [4, 162, 4, 1], [4, 162, 8, 1], [6, 8, 2, 1], [6, 8, 4, 1], [6, 32, 1, 1], [6, 72, 4, 1], [6, 72, 8, 2], [12, 72, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_2^3.C_2^5.C_2^4', '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': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '20736.z', 'autcentquo_hash': 687264991867046508, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3\\wr D_4:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 18, 10], [2, 81, 2], [3, 8, 6], [3, 32, 1], [4, 18, 8], [4, 162, 12], [6, 8, 6], [6, 32, 1], [6, 72, 20], [12, 72, 16]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '2592.ci', 'commutator_count': 1, 'commutator_label': '162.54', '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', '3.1'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 136, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 18, 1, 10], [2, 81, 1, 2], [3, 8, 1, 6], [3, 32, 1, 1], [4, 18, 2, 4], [4, 162, 1, 4], [4, 162, 2, 4], [6, 8, 1, 6], [6, 32, 1, 1], [6, 72, 1, 20], [12, 72, 2, 8]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 669614400, 'exponent': 12, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 0, 16], [8, 1, 8], [32, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2592.ci', 'hash': 1302982936702346125, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 2, 2, 2], 'inner_gens': [[2879290997287, 13208557023377, 9967165096320, 881929854847], [10862374523047, 4035153024017, 9434463056040, 38048774407], [8301859912927, 529859594897, 1328391555240, 204387127], [3314985463567, 4047607468817, 1328391555240, 204387127]], 'inner_hash': 1359974926057248800, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': True, 'inner_tex': 'C_3:S_3^3:C_2^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [4, 2], [8, 48], [32, 2]], 'label': '5184.ff', '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': 'C3^4:C4^2:C2^2', 'ngens': 4, '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, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 19, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 84, 'number_divisions': 68, 'number_normal_subgroups': 123, 'number_subgroup_autclasses': 341, 'number_subgroup_classes': 1550, 'number_subgroups': 52150, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 343], [3, 80], [4, 2088], [6, 1520], [12, 1152]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 8, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 2], 'outer_gen_pows': [0, 3412695607, 0, 1322056391160, 0, 0, 0], 'outer_gens': [[5412240980047, 13170711864977, 1328391555240, 37896364807], [1322052041640, 12332146997542, 9973500260400, 11950670970000], [2879290997280, 13208557023382, 1353873754927, 40682887], [5412240980047, 6722070138022, 9967165096320, 9992236116967], [2879290997280, 13208557023377, 1353873754920, 40682887], [2879290997280, 4035153024017, 1328391555240, 204387120], [2879290997287, 13208557023382, 1353873754920, 40682887]], 'outer_group': '128.928', 'outer_hash': 928, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 8, 'outer_perms': [11536, 34990, 5161, 40319, 7, 126, 5167], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\wr D_4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 2], [8, 32], [16, 8], [32, 2]], 'representations': {'PC': {'code': '13237474955693019835211643851857837929357421579314179653775101737706341762235319316769731580295519999072303437110876489666589', 'gens': [1, 2, 3, 5, 7, 8, 9], 'pres': [10, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 10921, 16442, 39072, 82, 79683, 63604, 2014, 52224, 13134, 144, 28805, 1935, 8665, 515, 286726, 26896, 71146, 1716, 3406, 322567, 667, 5797, 69868, 48638, 27588, 268, 18429, 43239, 23449]}, 'Perm': {'d': 16, 'gens': [2879290997287, 4035153024017, 1328391555240, 204387127]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 4], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^4:C_4^2:C_2^2', 'transitive_degree': 24, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 6, 'aut_exponent': 72, 'aut_gen_orders': [8, 2, 24, 12, 4, 4, 6, 3, 3, 3], 'aut_gens': [[167265, 167528, 29606670, 377242909, 263727360], [1786240, 328985, 42030622, 323660451, 462940739], [351550185, 216201502, 127390100, 376235196, 127387583], [29605311, 3109, 252637972, 323372379, 315159500], [339619620, 127411199, 40284847, 287279885, 389467855], [163720224, 174988800, 163699712, 43360799, 427339114], [1498112, 1785633, 324869904, 215274239, 263727360], [29438790, 349183008, 29727661, 43360799, 252637972], [167265, 2949352, 14923545, 377242909, 263727360], [167265, 3116432, 29606670, 42030622, 101873059], [167265, 1785633, 331503, 43360799, 426318404]], 'aut_group': '186624.fv', 'aut_hash': 7594661418670414184, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 186624, 'aut_permdeg': 162, 'aut_perms': [9483350386739549299325899184429142727703679328353310733335772123543244394913048009492188313327206440079094896796612830726660109423483768205266250679090072641612008431255793701022753349023106293328683222932026347328949870303396079493462913916449801467062395849819535259210452085534623283657, 162657991845475582805012522214499748822161953498927029472343322886173445315311217130459518479938037385602874110607785933138857775556434207428894036131932838925557194186207234578550068103057058329361508260935163870501938608243698657238637560915965394577393359479389027535273090361621499031, 3990432115934678121741132412573111166276989857547308005964847094222842917110577450935168872960475701884141250995551865050408256369212074094873863027439253204768469323805366635875246962853150811226631238422675635442747585681277348045252188735391873792398028943168711900243639387557622877847, 4687524190325351122530849645224760042014707299793681080456890509786036153611501635109609012792058724619836220003958190990517339577794238329885694696649307933309410974523698988436995848263337885484024365564978546198357133723235629274957162262067552501684193320890420485631269875032875360154, 8532320192489185870284043294075118500099483859665840943363253512027462049077175577294217243344865528542288847631977948533089345396069279652317906770540470394342387019672039443626768787267882806025195895448736111280105849799833377359423218866794521801133320164182939526374447844829197167464, 4535530246995223206017645037982969380715539824910388096526357890505719212020410764392205402959151102182263405556856391289241520588105806068723991356476811686061107129239936623337964436344205151916702094920177191776884002986991952202329321454900570465726233701623059042141488694848594072309, 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1422627312146663629699833451850332575504022052084668311391561464184358122841586199195430271936902053451457899010924623393318052964861868572154890481347655573727469298735750691971689088331749884995754592704221734147150935900032255374961470141117299427441630552272365451328995564288143446405], 'aut_phi_ratio': 216.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 9, 1], [2, 81, 1, 1], [3, 8, 6, 1], [3, 32, 1, 1], [4, 162, 6, 1], [6, 72, 18, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:S_3.S_4\\wr C_2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '186624.fv', 'autcentquo_hash': 7594661418670414184, 'autcentquo_nilpotent': False, 'autcentquo_order': 186624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:S_3.S_4\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 18, 9], [2, 81, 1], [3, 8, 6], [3, 32, 1], [4, 162, 6], [6, 72, 18]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2592.ci', 'commutator_count': 1, 'commutator_label': '162.54', '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', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 61, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 9], [2, 81, 1, 1], [3, 8, 1, 6], [3, 32, 1, 1], [4, 162, 1, 6], [6, 72, 1, 18]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 74401600, 'exponent': 12, 'exponents_of_order': [5, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 24], [32, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2592.ci', 'hash': 1359974926057248800, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 2, 2, 2, 2], 'inner_gens': [[167265, 592, 29439589, 374944015, 278568107], [328449, 167528, 29606670, 377242909, 412659706], [328449, 167528, 29606670, 43545599, 263727360], [1498112, 167528, 163699712, 377242909, 263727360], [14926470, 189504870, 29606670, 377242909, 263727360]], 'inner_hash': 1359974926057248800, 'inner_nilpotent': False, 'inner_order': 2592, 'inner_split': True, 'inner_tex': 'C_3:S_3^3:C_2^2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [4, 1], [8, 24], [32, 1]], 'label': '2592.ci', '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:S3^3:C2^2', 'ngens': 5, '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, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 7, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 42, 'number_divisions': 42, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 70, 'number_subgroup_classes': 666, 'number_subgroups': 19770, 'old_label': None, 'order': 2592, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 243], [3, 80], [4, 972], [6, 1296]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 3, 3], 'outer_gen_pows': [23616, 87102736, 127387583, 87103024, 40287205], 'outer_gens': [[29605311, 101883498, 331503, 155341148, 323660451], [177316177, 216201502, 252639460, 216080047, 278568107], [177316177, 426194314, 43378071, 437080912, 377242909], [177316177, 426194314, 446975699, 29439589, 163699305], [190866170, 277535589, 153882524, 277413213, 314069540]], 'outer_group': '72.40', 'outer_hash': 40, 'outer_nilpotent': False, 'outer_order': 72, 'outer_permdeg': 6, 'outer_perms': [136, 633, 687, 662, 543], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': '\\SOPlus(4,2)', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 12, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [4, 1], [8, 24], [32, 1]], 'representations': {'PC': {'code': '43749690043031551989739373248629011842984585004995929638275743960464568109305474105485327', 'gens': [1, 2, 3, 5, 7, 8, 9], 'pres': [9, -2, -2, -2, -2, 2, -3, 3, 3, 3, 173, 74, 16924, 26482, 2101, 130, 15557, 2615, 464, 60486, 6063, 528, 1545, 2311, 34585, 5218, 2635, 139976, 70001, 7154, 17531, 9278]}, 'Perm': {'d': 12, 'gens': [377242909, 167528, 167265, 29606670, 263727360]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 12, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3:S_3^3:C_2^2', 'transitive_degree': 12, 'wreath_data': None, 'wreath_product': False}
