Formats: - HTML - YAML - JSON - 2026-07-23T04:45:20.362227
  • gps_subgroup_search • Show schema
    {'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '41472.m', 'ambient_counter': 13, 'ambient_order': 41472, 'ambient_tex': '\\SOPlus(4,2)^2.D_4', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 2592, 'counter': 52, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '41472.m.8.y1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '8.y1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': None, 'quotient_Agroup': None, 'quotient_abelian': None, 'quotient_cyclic': None, 'quotient_hash': None, 'quotient_metabelian': None, 'quotient_nilpotent': None, 'quotient_order': 8, 'quotient_simple': None, 'quotient_solvable': None, 'quotient_supersolvable': None, 'quotient_tex': None, 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '5184.qq', 'subgroup_hash': 3787923027923722955, 'subgroup_order': 5184, 'subgroup_tex': 'C_3^3:C_{12}:\\SD_{16}', 'supersolvable': False, 'sylow': 0}
  • gps_subgroup_data • Show schema
    {'ambient': '41472.m', 'aut_centralizer_order': None, 'aut_label': '8.y1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '41472.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['4.c1', '4.m1', '4.o1'], 'contains': ['16.a1', '16.z1', '16.bc1', '16.ca1', '16.cd1', '72.z1', '72.ba1'], 'core': '16.a1', 'coset_action_label': None, 'count': 2, 'diagramx': [6339, -1, 5709, -1], 'generators': [1134035330171593, 77321, 1864844282666737, 228132, 40319, 64339019542644, 2849517333962532, 9680, 2618239550613119, 17137], 'label': '41472.m.8.y1', 'mobius_quo': None, 'mobius_sub': 0, 'normal_closure': '4.c1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '2.b1', 'old_label': '8.y1', 'projective_image': '41472.m', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.y1', 'subgroup_fusion': None, 'weyl_group': None}
  • gps_groups • Show schema
    {'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, 2, 4, 12, 24], 'aut_gens': [[224189, 45507, 268240896693, 338677, 63975, 219574, 368871149493, 19203650492, 287404882998, 267762188598], [5515, 184197, 19200111233, 33770, 13146, 276480, 361726172033, 181062922172, 281174044506, 19203714906], [317372, 45507, 180583603893, 157572, 72949, 321987, 361726042293, 19203650492, 199308427454, 181062821054], [5515, 138690, 456053257212, 24202, 37817, 357364, 3817212, 200222986172, 287404657481, 286482942281], [362879, 219574, 448907966765, 285303, 105306, 45507, 180583608365, 193999282315, 268244860960, 200223004960], [5515, 80884, 361726363894, 24202, 26719, 219574, 268241218294, 280259763595, 193077911333, 286483223333]], 'aut_group': None, 'aut_hash': 2723700116397070647, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 20736, 'aut_permdeg': 180, 'aut_perms': [102160795788382766317075901219282483933466926291090762142792928052048165729302452645084371299771209460688719143906543503802884053984641959881013318341795496385218431722059829111145666500928636718930601535461571038532421216576462319228570896487772262016152025442980032801393286008643167240995038254140256159547824651800161126063398, 10676265874787028802249791439991804994375494449974649030780311723870016482378364994977690992947639212316796596193384957667397536315632458389166886680878079662211365514142530663179851032309485454282316887515012703393681662047630710440023954348704929323320477031862834208293333390784458636711930362740374935779851211566180751289424, 133027158220574544416832889082967439970757359033587270683519543182099549865298456629538765645475865696853991792760773877699232868853794359158637463069263531907994921917466799774550831219466752695116118191130778880214158740913833763789732643291714311867085493066809024001961247537258270049924323164677877005282004585099643062803553, 85600394158897513189536688677917250849921981195057766501936670821988824543599309688026493586714784532585675409784842045377500113168476567764472067999017953947121768874288832844733273426474593149288204449250721921800257058864099221508677271853072951272283726906605506225599050242875494708806717196651679066516825776310444797941354, 184185653884689805790258718328516564482278775020466173158986450870278020908780321546524721851656494641865880561862959099742122879206488919517220534098231772039149681819289994199296313085395461905019813929346418316825619642194703491839375168057908949966952535637083264823697492280393009860904618516801896089454623399478676954467216], 'aut_phi_ratio': 12.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 72, 2, 1], [2, 81, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [3, 32, 2, 1], [4, 18, 1, 2], [4, 36, 1, 1], [4, 162, 1, 2], [4, 324, 1, 2], [4, 324, 2, 1], [6, 36, 2, 1], [6, 72, 1, 1], [6, 144, 2, 2], [6, 288, 2, 1], [8, 108, 2, 2], [12, 72, 2, 1], [12, 144, 1, 1], [12, 144, 2, 1], [24, 216, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.C_4^2.C_2^4', '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': 24, 'autcentquo_group': None, 'autcentquo_hash': 2723700116397070647, 'autcentquo_nilpotent': False, 'autcentquo_order': 20736, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.D_4^2.C_2^2', 'cc_stats': [[1, 1, 1], [2, 9, 2], [2, 72, 2], [2, 81, 1], [3, 4, 2], [3, 8, 1], [3, 32, 2], [4, 18, 2], [4, 36, 1], [4, 162, 2], [4, 324, 4], [6, 36, 2], [6, 72, 1], [6, 144, 4], [6, 288, 2], [8, 108, 4], [12, 72, 2], [12, 144, 3], [24, 216, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '5184.qq', 'commutator_count': 1, 'commutator_label': '648.715', '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': 433, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 9, 1, 2], [2, 72, 1, 2], [2, 81, 1, 1], [3, 4, 1, 2], [3, 8, 1, 1], [3, 32, 1, 2], [4, 18, 1, 2], [4, 36, 1, 1], [4, 162, 1, 2], [4, 324, 1, 2], [4, 324, 2, 1], [6, 36, 1, 2], [6, 72, 1, 1], [6, 144, 1, 4], [6, 288, 1, 2], [8, 108, 2, 2], [12, 72, 1, 2], [12, 144, 1, 3], [24, 216, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 2150400, 'exponent': 24, 'exponents_of_order': [6, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 1, 4]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '5184.qq', 'hash': 3787923027923722955, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 3, 2, 4, 4, 3, 2, 6, 4, 12], 'inner_gens': [[224189, 80884, 268241218294, 338677, 63975, 321987, 368871471094, 19203891595, 287404785526, 267762091126], [178682, 45507, 268240896693, 108554, 294198, 219574, 368871149493, 19203615115, 287404785526, 267762091126], [317372, 45507, 268240896693, 157572, 72949, 321987, 88698759093, 19203650492, 287404805054, 181062821054], [224189, 321987, 268240981706, 338677, 166153, 45507, 368871234506, 19203695999, 287404931606, 267762237206], [224189, 184197, 268241026433, 254325, 63975, 138690, 368871279233, 19203752905, 287404741624, 267762047224], [5515, 45507, 268241218294, 33770, 20073, 219574, 368871471094, 19203972479, 287404839096, 267762144696], [317372, 45507, 19199981493, 157572, 72949, 321987, 368871149493, 181062645692, 19679198654, 25427217854], [281995, 80884, 268240896693, 307699, 325062, 321987, 448907962293, 19203650492, 281174034039, 267761989239], [362879, 184197, 268241159803, 285303, 227590, 138690, 448908225403, 25427283595, 287404882998, 181062898998], [362879, 184197, 479265403, 285303, 227590, 138690, 448908225403, 19203891595, 25909926198, 267762188598]], 'inner_hash': 3787923027923722955, 'inner_nilpotent': False, 'inner_order': 5184, 'inner_split': False, 'inner_tex': 'C_3^3:C_{12}:\\SD_{16}', 'inner_used': [1, 2, 3, 4, 5, 7, 8], 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': 32, 'irrR_degree': 32, 'irrep_stats': [[1, 8], [2, 10], [4, 9], [8, 10], [16, 1], [32, 4]], 'label': '5184.qq', 'linC_count': 32, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 32, 'linR_count': 32, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^3:C12:SD16', 'ngens': 10, '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': 28, 'number_characteristic_subgroups': 29, 'number_conjugacy_classes': 42, 'number_divisions': 37, 'number_normal_subgroups': 37, 'number_subgroup_autclasses': 347, 'number_subgroup_classes': 540, 'number_subgroups': 23564, 'old_label': None, 'order': 5184, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 243], [3, 80], [4, 1692], [6, 1296], [8, 432], [12, 576], [24, 864]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 281173939200], 'outer_gens': [[224189, 80884, 268240896693, 254325, 118879, 219574, 368871149493, 25427087999, 268244828603, 181062908603], [224189, 80884, 368871471094, 338677, 63975, 321987, 268241218294, 193999558795, 25909828726, 200222865526]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 4], [4, 12], [8, 6], [16, 3], [32, 4]], 'representations': {'PC': {'code': '9805185608305814152387375585748554869752858357649366677749176151986030611432305957221308135741436821944064027272808182679443495', 'gens': [1, 2, 5, 6, 9, 10], 'pres': [10, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 2041, 51, 842, 82, 8643, 19204, 10414, 4824, 234, 10565, 16335, 6745, 1835, 175, 21286, 17936, 5626, 4236, 206, 2567, 16017, 347, 3877, 181458, 5458, 1148, 460809, 172819, 4859, 3669]}, 'Perm': {'d': 15, 'gens': [224189, 45507, 268240896693, 338677, 63975, 219574, 368871149493, 19203650492, 287404882998, 267762188598]}}, 'schur_multiplier': [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_3^3:C_{12}:\\SD_{16}', 'transitive_degree': 48, 'wreath_data': None, 'wreath_product': False}
  • gps_groups • Show schema
    {'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': 4, 'aut_exponent': 48, 'aut_gen_orders': [4, 4, 8], 'aut_gens': [[3514922837851602, 2581710453170261, 2135719723867333], [4200050242550957, 2179047813585380, 129921523661554], [4516526639669097, 2954056040260558, 2135719723798883], [6332792013425709, 1073775495640382, 2513698892136133]], 'aut_group': '41472.m', 'aut_hash': 7917341340725978817, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 204, 'aut_perms': [1309345485919600749745934577640419337302230733088758364920560568185301816444415756636074728040140178233024704690984694709862097595294845047978309409911408501512987974428598771665713645519250301391504222859685660769941573225096562774513043862322495811203297779939781931589486409854710028129740049070633453128132184482379391463902054065372251089684139270315952799577249615940864675838487, 2594606410385872344599837413985881538830504448751372070418139790425258970876659336254484712044212191744353759717762566046587065395239653399888212617774726309440990757678281773420115186558808454413667598590162740679766065633083736402834173298455471960961555635753495248571306121897555846729329965983667496301954923938954752109255553652165252643249479520279574283766879335840008859114, 1194328403875403437524957653684777636902823975383181744178389705632957166665117555029927556289489547622267908098473537423880585006004329630912057855203433722666346627750545155898096857477041711591529215985159004915113844333031344192605063754373054866973389228924927652503254496566452286516980830520382233405637361200079713509790150485630812880310866196271095149338244099960157621946915], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 24, 1, 1], [2, 81, 1, 1], [2, 144, 1, 2], [2, 216, 1, 1], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 1], [4, 72, 1, 1], [4, 324, 1, 2], [4, 432, 1, 1], [4, 648, 1, 1], [4, 864, 1, 1], [4, 1296, 1, 3], [4, 1728, 1, 1], [6, 48, 1, 1], [6, 144, 1, 1], [6, 192, 1, 1], [6, 384, 1, 1], [6, 432, 1, 1], [6, 576, 1, 2], [6, 1152, 1, 1], [8, 36, 1, 2], [8, 324, 1, 4], [8, 432, 1, 2], [8, 648, 1, 3], [8, 1296, 1, 2], [8, 2592, 1, 1], [8, 5184, 1, 1], [12, 288, 1, 1], [12, 576, 1, 1], [12, 864, 1, 1], [12, 1728, 1, 1], [12, 3456, 1, 1], [16, 2592, 1, 2], [24, 288, 1, 2], [24, 864, 1, 2]], 'aut_supersolvable': False, 'aut_tex': '\\SOPlus(4,2)^2.D_4', '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': 48, 'autcentquo_group': '41472.m', 'autcentquo_hash': 7917341340725978817, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '\\SOPlus(4,2)^2.D_4', 'cc_stats': [[1, 1, 1], [2, 18, 1], [2, 24, 1], [2, 81, 1], [2, 144, 2], [2, 216, 1], [3, 16, 1], [3, 64, 1], [4, 36, 1], [4, 72, 1], [4, 324, 2], [4, 432, 1], [4, 648, 1], [4, 864, 1], [4, 1296, 3], [4, 1728, 1], [6, 48, 1], [6, 144, 1], [6, 192, 1], [6, 384, 1], [6, 432, 1], [6, 576, 2], [6, 1152, 1], [8, 36, 2], [8, 324, 4], [8, 432, 2], [8, 648, 3], [8, 1296, 2], [8, 2592, 1], [8, 5184, 1], [12, 288, 1], [12, 576, 1], [12, 864, 1], [12, 1728, 1], [12, 3456, 1], [16, 2592, 2], [24, 288, 2], [24, 864, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '41472.m', 'commutator_count': 1, 'commutator_label': '5184.pf', 'complements_known': True, 'complete': True, 'complex_characters_known': True, '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'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 18, 1, 1], [2, 24, 1, 1], [2, 81, 1, 1], [2, 144, 1, 2], [2, 216, 1, 1], [3, 16, 1, 1], [3, 64, 1, 1], [4, 36, 1, 1], [4, 72, 1, 1], [4, 324, 1, 2], [4, 432, 1, 1], [4, 648, 1, 1], [4, 864, 1, 1], [4, 1296, 1, 3], [4, 1728, 1, 1], [6, 48, 1, 1], [6, 144, 1, 1], [6, 192, 1, 1], [6, 384, 1, 1], [6, 432, 1, 1], [6, 576, 1, 2], [6, 1152, 1, 1], [8, 36, 2, 1], [8, 324, 2, 2], [8, 432, 2, 1], [8, 648, 1, 1], [8, 648, 2, 1], [8, 1296, 2, 1], [8, 2592, 1, 1], [8, 5184, 1, 1], [12, 288, 1, 1], [12, 576, 1, 1], [12, 864, 1, 1], [12, 1728, 1, 1], [12, 3456, 1, 1], [16, 2592, 2, 1], [24, 288, 2, 1], [24, 864, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 564264960, 'exponent': 48, 'exponents_of_order': [9, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 8], [32, 0, 4], [32, 1, 2], [64, 1, 4], [128, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '41472.m', 'hash': 7917341340725978817, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [4, 4, 8], 'inner_gens': [[3514922837851602, 1199231319751772, 2887451422921836], [4894530313270472, 2581710453170261, 796566727974047], [4849814994939732, 2954056040229783, 2135719723867333]], 'inner_hash': 7917341340725978817, 'inner_nilpotent': False, 'inner_order': 41472, 'inner_split': True, 'inner_tex': '\\SOPlus(4,2)^2.D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 16, 'irrR_degree': 16, 'irrep_stats': [[1, 8], [2, 6], [4, 18], [8, 3], [16, 8], [32, 6], [64, 4], [128, 1]], 'label': '41472.m', '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': True, 'name': 'SO+(4,2)^2.D4', 'ngens': 3, '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, 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': 31, 'number_conjugacy_classes': 54, 'number_divisions': 45, 'number_normal_subgroups': 31, 'number_subgroup_autclasses': 1431, 'number_subgroup_classes': 1431, 'number_subgroups': 227218, 'old_label': None, 'order': 41472, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 627], [3, 80], [4, 8316], [6, 3504], [8, 14544], [12, 6912], [16, 5184], [24, 2304]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, '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': 7, 'perfect': False, 'permutation_degree': 18, '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, 6], [8, 7], [16, 9], [32, 2], [64, 6], [128, 1]], 'representations': {'PC': {'code': '608206385848814155080286995649919776217912322121576815200009590529477716958513242942021562003967954107832242606694721154374797199536696894112922620338057991926128524858919128409892167136808445715415033012375710812472058515584327639713597979999482160936061333504564387465913675203251471586505989284631618338479947866127', 'gens': [1, 2, 4, 7, 11, 12, 13], 'pres': [13, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 226720, 627277, 66, 775790, 926435, 276864, 180053, 146, 19764, 1008297, 458410, 186, 2678213, 1558770, 280207, 2614982, 1112039, 27696, 262853, 119814, 33741, 266, 1504263, 674772, 23329, 401070, 233851, 17128, 306, 3384584, 1873893, 295823, 144204, 15985, 346, 1930249, 199702, 457648, 233021, 4234, 1098250, 73239, 164785, 96158, 13803, 10384, 12113, 1830, 958475, 1078296, 479269, 149810, 119871, 45004, 26297, 15078, 5731, 2422796, 1038361, 1189798, 21683, 156896, 146093]}, 'Perm': {'d': 18, 'gens': [2581710453170261, 2135719723867333, 3514922837851602]}}, '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': '\\SOPlus(4,2)^2.D_4', 'transitive_degree': 18, 'wreath_data': ['288.bd1', '20736.e1', '41472.a1', '2T1'], 'wreath_product': True}