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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1152.12051', 'ambient_counter': 12051, 'ambient_order': 1152, 'ambient_tex': '(C_2\\times C_6^2):\\SD_{16}', 'central': True, 'central_factor': False, 'centralizer_order': 1152, 'characteristic': True, 'core_order': 2, 'counter': 425, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1152.12051.576.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '576.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '576.8300', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 8300, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 576, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:\\SD_{16}', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U2'], 'split': False, 'standard_generators': False, 'stem': True, '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': '1152.12051', 'aut_centralizer_order': 4608, 'aut_label': '576.a1', 'aut_quo_index': 4, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 4608, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['192.a1.a1', '288.a1.a1', '288.b1.a1', '288.c1.a1', '288.d1.a1', '288.e1.a1', '288.f1.a1'], 'contains': ['1152.a1.a1'], 'core': '576.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4314, 3288, 4039, 2847, 4778, 6650, 5043, 3314], 'generators': [576], 'label': '1152.12051.576.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '576.a1.a1', 'normal_contained_in': ['64.a1.a1', '288.a1.a1'], 'normal_contains': ['1152.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '576.a1.a1', 'projective_image': '576.8300', 'quotient_action_image': '1.1', 'quotient_action_kernel': '576.8300', 'quotient_action_kernel_order': 576, 'quotient_fusion': None, 'short_label': '576.a1.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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [4, 2, 4, 4, 4, 6], 'aut_gens': [[1, 2, 16, 96, 576], [601, 242, 272, 704, 576], [401, 658, 80, 480, 576], [849, 246, 16, 1072, 576], [261, 694, 1008, 320, 576], [1021, 22, 1040, 160, 576], [977, 130, 16, 96, 576]], 'aut_group': None, 'aut_hash': 7948342299425870836, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 4608, 'aut_permdeg': 192, 'aut_perms': [170448576834055697648100723223909402879270630230347151430172151925490394878888236020476469501009132808360461389049738901055458547121882356736584048582451386162520339363390174225920101580049038699454909331152343077109674002769470139229528719048717404991388857968898784781055364625667538996408840895642637242646652889903123172552184173250245649732506099982749, 137465039704577755923245917400585042764857162361725791999807948738480321894348687502729275900132698942117721773934714086393845006936005829618474878173471483226035637144293687949520609882229906728369368682679942217357543135743206511838239761296171758524095258729918780525667888535267820849217660539692908756771530979132720276783949655301197457588526038801701, 225750322506465041117433598714247933681481515629943473823209748982323643609494858150076541757294196532427264338967163033380538037961375300453792363461570491908095177548093501714424099569985495572953463766183484102120650101864725537209640183896411030768377120503914806173809343879745530911398389010389764752662064979861492874072550307738612157080188894592161, 143871472620071170264449466766142989800247727505536730294684082972065279554734396073361195550606919617901213124836160600060853258007069079683430050963527581976914004637652563224394753586951377242595834507798125300352055154921347376504574529468226666673936161895860314950038968294367869163967610292724437780161715563774104594466607230376724023063764957701284, 180156553882054514963521678744867492934037121826808410231252029768435055749267087561076332105766755105089341311834438513797144261308594533014415829870807983087205214935217278202014140776507394361464960465488563899346976624370738975778577064747903988460153986221921035203902187405386511018010573909627285557246162875699150081498376580199296116289490184209419, 293176813380316539238087775270347090567049816680383819368567672603264724819738818013844621513433606483279527626561515591481222368890113363715013197348389179557540083922456685837479534569982937313489191366287671991251735949833778687361698828197837641888699130773231759004789168783806231307331615749839042350032281195792225453895335677534344352149066392773401], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 24, 2, 1], [2, 36, 1, 1], [3, 8, 1, 1], [4, 24, 2, 1], [4, 36, 2, 1], [4, 72, 1, 1], [4, 72, 2, 2], [6, 8, 1, 3], [6, 16, 2, 1], [6, 48, 2, 1], [8, 72, 2, 2], [12, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_2^5.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '576.8299', 'autcentquo_hash': 8299, 'autcentquo_nilpotent': False, 'autcentquo_order': 576, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:\\SD_{16}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 9, 2], [2, 18, 1], [2, 24, 2], [2, 36, 1], [3, 8, 1], [4, 24, 2], [4, 36, 2], [4, 72, 5], [6, 8, 3], [6, 16, 2], [6, 48, 2], [8, 72, 4], [12, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '576.8300', 'commutator_count': 1, 'commutator_label': '144.191', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 12051, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 24, 1, 2], [2, 36, 1, 1], [3, 8, 1, 1], [4, 24, 1, 2], [4, 36, 1, 2], [4, 72, 1, 5], [6, 8, 1, 3], [6, 16, 1, 2], [6, 48, 1, 2], [8, 72, 2, 2], [12, 48, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 107520, 'exponent': 24, 'exponents_of_order': [7, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 4], [16, 1, 1]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '288.1027', 'hash': 12051, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 8, 6, 6, 1], 'inner_gens': [[1, 6, 16, 496, 576], [13, 2, 784, 368, 576], [1, 962, 16, 96, 576], [273, 402, 16, 96, 576], [1, 2, 16, 96, 576]], 'inner_hash': 8300, 'inner_nilpotent': False, 'inner_order': 576, 'inner_split': True, 'inner_tex': 'C_6^2:\\SD_{16}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 10], [4, 5], [8, 8], [16, 2]], 'label': '1152.12051', 'linC_count': 4, 'linC_degree': 8, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 4, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C2*C6^2):SD16', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 33, 'number_divisions': 31, 'number_normal_subgroups': 38, 'number_subgroup_autclasses': 294, 'number_subgroup_classes': 434, 'number_subgroups': 5632, 'old_label': None, 'order': 1152, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 127], [3, 8], [4, 480], [6, 152], [8, 288], [12, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 8], 'outer_gens': [[49, 290, 16, 96, 576], [577, 2, 80, 480, 576], [9, 2, 400, 544, 576]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 7], [8, 8], [16, 2]], 'representations': {'PC': {'code': '265443540732020777746274526151045319022467359582409123959888204257785457674', 'gens': [1, 2, 5, 7, 9], 'pres': [9, 2, 2, 2, 2, 2, 3, 2, 3, 2, 109, 46, 326, 74, 17653, 3082, 481, 130, 11246, 6071, 464, 31254, 11607, 11112, 3813, 186, 29959, 2320, 4633, 3490]}, 'Perm': {'d': 17, 'gens': [2965059823492, 1596153451638, 526, 4359920113048, 3043, 5599050083778, 18498, 26354196288000, 44842333898880]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_6^2):\\SD_{16}', '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': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 24, 'aut_gen_orders': [8, 8, 6, 4, 4], 'aut_gens': [[1, 2, 16, 96], [549, 370, 144, 544], [301, 66, 112, 352], [97, 70, 176, 96], [9, 274, 176, 160], [77, 454, 240, 352]], 'aut_group': None, 'aut_hash': 307816269953595676, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2304, 'aut_permdeg': 96, 'aut_perms': [695837472746545833767828856352007529324947448835107073740090150263565778836094278511304392858838230745625297688531381355084729074012812751981856035939, 820215115426975117330292345556029833764445910813517733648307883741468589190444520469877147468143365237449962253213635399155769238724733910948542295151, 718308900806127802925538720991764470563853417488678504085687346070842463242870876296231115285365625065603320188880342206136307323529876980944392178073, 473493673910231955337993976624786760755494564829165462666426178039194769867304735019187951922391026427062669722350045371012051657346167844245881190214, 147305437697979690970967439058864190458579679074668243473956070445592632594826551179640662368342846314394668658132263399827187241976622004434752179138], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 24, 1, 1], [3, 8, 1, 1], [4, 18, 2, 1], [4, 24, 1, 1], [4, 36, 1, 1], [4, 36, 4, 1], [6, 8, 1, 1], [6, 16, 1, 1], [6, 48, 1, 1], [8, 36, 2, 2], [12, 48, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3:S_3.C_2^5.C_2^2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '288.1027', 'autcentquo_hash': 1027, 'autcentquo_nilpotent': False, 'autcentquo_order': 288, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_9:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 9, 2], [2, 18, 1], [2, 24, 1], [3, 8, 1], [4, 18, 2], [4, 24, 1], [4, 36, 5], [6, 8, 1], [6, 16, 1], [6, 48, 1], [8, 36, 4], [12, 48, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '288.1027', 'commutator_count': 1, 'commutator_label': '72.45', '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'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8300, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 9, 1, 2], [2, 18, 1, 1], [2, 24, 1, 1], [3, 8, 1, 1], [4, 18, 1, 2], [4, 24, 1, 1], [4, 36, 1, 5], [6, 8, 1, 1], [6, 16, 1, 1], [6, 48, 1, 1], [8, 36, 2, 2], [12, 48, 1, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 26880, 'exponent': 24, 'exponents_of_order': [6, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '288.1027', 'hash': 8300, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 8, 6, 3], 'inner_gens': [[1, 6, 496, 480], [13, 2, 560, 320], [97, 130, 16, 96], [193, 450, 16, 96]], 'inner_hash': 1027, 'inner_nilpotent': False, 'inner_order': 288, 'inner_split': True, 'inner_tex': 'F_9:C_2^2', 'inner_used': [1, 2, 3], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 10], [4, 1], [8, 4], [16, 1]], 'label': '576.8300', 'linC_count': 16, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 16, 'linQ_dim': 10, 'linQ_dim_count': 16, 'linR_count': 16, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:SD16', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 18, 'number_characteristic_subgroups': 20, 'number_conjugacy_classes': 24, 'number_divisions': 22, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 129, 'number_subgroup_classes': 185, 'number_subgroups': 1630, 'old_label': None, 'order': 576, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 63], [3, 8], [4, 240], [6, 72], [8, 144], [12, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [12, 8], 'outer_gens': [[5, 2, 432, 544], [5, 50, 240, 128]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [6, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 6], [4, 3], [8, 4], [16, 1]], 'representations': {'PC': {'code': 82162789284050570911263005399289659411168295826497932648760842351662597, 'gens': [1, 2, 5, 7], 'pres': [8, 2, 2, 2, 2, 2, 3, 2, 3, 97, 41, 290, 66, 19844, 11212, 4660, 428, 116, 19973, 10765, 3093, 413, 26886, 8974, 2262, 3390, 166, 24583, 2063, 3607, 3103]}, 'Perm': {'d': 13, 'gens': [95605329, 142259885, 7, 178185016, 16, 223347720, 698629800, 1221138120]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:\\SD_{16}', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
