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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '6718464.bbw', 'ambient_counter': 725, 'ambient_order': 6718464, 'ambient_tex': 'C_3^8:C_4^2.Q_{16}:C_2^2', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 1679616, 'counter': 31, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '6718464.bbw.4._.O', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.O', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '1679616.yh', 'subgroup_hash': None, 'subgroup_order': 1679616, 'subgroup_tex': 'C_3^8.C_4:\\OD_{16}.C_2^2', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '6718464.bbw', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [117635899382695670896743841444951675918076, 376703666980290, 20962878091100235933258515839342491697797, 63822384498269430727129924222762399012290, 21210673760395, 3243086199688471728464077307, 418829649741950392737872884, 233429858751468248293285255275731225592679, 10628652128250503819036102992460278548480, 822228046644134973649184189, 127943795798488762033504738607430089124920, 276480, 1845584622685684, 219574, 1258350440040947635195968000, 72654371322884864975018568834369420981909], 'label': '6718464.bbw.4._.O', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '4.O', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4._.O', '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': '8.2', 'all_subgroups_known': None, 'almost_simple': None, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[370499269349287506978852091461450846433629, 212139679869269128555810056572826433201481], [159558932169268623737856137473251792885464, 212139679869269128555810056572826433201481], [298471379949874392357436411799549305045206, 33076072994754523485348241759174240678917], [328592781188793549795789450169444748977440, 212139679869270277603665437190364379057862], [298757698935096383141115228791913314144491, 223679290928456276856348530173080385457862], [299339457343102266570785270646717305174236, 223679290928456276856348527644991766212681], [299339457343104767491361748858227627394473, 212139679869269128555810056572826433201481], [287834587485755762545353238561432277634759, 223679290928457425904203908262529712069062], [319683952484838415076035169866458652751836, 212139679869269128555810056572826433201481], [340958080650928376350937816753683929996999, 202101509785389061291006349060481222221689], [287834587485757860256676348058873961173106, 244050057261617050815205833195519074092217], [319683952484840125058808676362645600934876, 202101509785387434602255684755845500716040], [298471379949871875818718981411463014375276, 255295242155406813063995741934246746322440], [340958080650927988622388212409695697897159, 265923894283654800344314412640033626353304], [319683952484838415076035169119714398479559, 212139679869269128555810056572826433342855], [359861933647314498338198261829477077404636, 191472857657139447321937013462662754435606], [359861933647314498338198259739999326203506, 212139679869269128555810056572826433475606], [330320744948954528349400914806154909555399, 192097250422253383600136778853224749630654], [289301820947365128214956757706697386198429, 212139679869269128555810056572826433201481], [371054969051094599159676757912205806611399, 212139679869269948120889624673294595909054]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 13436928, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 24.0, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 6561, 1, 1], [3, 32, 1, 1], [3, 64, 1, 2], [3, 64, 2, 1], [3, 128, 1, 1], [3, 256, 2, 6], [3, 256, 4, 3], [4, 324, 1, 1], [4, 5832, 1, 1], [4, 11664, 2, 1], [4, 13122, 1, 2], [4, 26244, 1, 2], [6, 2592, 1, 1], [6, 2592, 2, 1], [6, 5184, 1, 2], [6, 5184, 2, 1], [6, 10368, 1, 1], [8, 52488, 2, 1], [8, 104976, 1, 3], [8, 104976, 4, 1], [12, 2592, 1, 2], [12, 5184, 2, 2], [12, 23328, 2, 1], [12, 46656, 4, 1], [16, 104976, 4, 1]], 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 162, 1], [2, 324, 1], [2, 6561, 1], [3, 32, 1], [3, 64, 4], [3, 128, 1], [3, 256, 24], [4, 324, 1], [4, 5832, 1], [4, 11664, 2], [4, 13122, 2], [4, 26244, 2], [6, 2592, 3], [6, 5184, 4], [6, 10368, 1], [8, 52488, 2], [8, 104976, 7], [12, 2592, 2], [12, 5184, 4], [12, 23328, 2], [12, 46656, 4], [16, 104976, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '1679616.yh', 'commutator_count': 1, 'commutator_label': '209952.bj', 'complements_known': None, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 16, 'conjugacy_classes_known': True, 'counter': 632, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 6561, 1, 1], [3, 32, 1, 1], [3, 64, 1, 4], [3, 128, 1, 1], [3, 256, 1, 24], [4, 324, 1, 1], [4, 5832, 1, 1], [4, 11664, 2, 1], [4, 13122, 1, 2], [4, 26244, 1, 2], [6, 2592, 1, 3], [6, 5184, 1, 4], [6, 10368, 1, 1], [8, 52488, 2, 1], [8, 104976, 1, 1], [8, 104976, 2, 3], [12, 2592, 2, 1], [12, 5184, 2, 2], [12, 23328, 2, 1], [12, 46656, 2, 2], [16, 104976, 4, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 48, 'exponents_of_order': [8, 8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 0, 4], [32, 1, 4], [64, 0, 8], [64, 1, 8], [128, 1, 2], [256, 1, 24]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1679616.yh', 'hash': 504442062718423139, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [16, 8], 'inner_gens': [[370499269349287506978852091461450846433629, 33076072994752851974776642900503371161204], [159558932169268623737856137473251792885464, 212139679869269128555810056572826433201481]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 1679616, 'inner_split': None, 'inner_tex': 'C_3^8.C_4:\\OD_{16}.C_2^2', 'inner_used': None, 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 10], [4, 5], [8, 2], [32, 8], [64, 16], [128, 2], [256, 24]], 'label': '1679616.yh', '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': None, 'metabelian': False, 'metacyclic': False, 'monomial': None, 'name': 'C3^8.C4:OD16.C2^2', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': None, 'normal_index_bound': None, 'normal_order_bound': None, 'normal_subgroups_known': None, 'number_autjugacy_classes': 43, 'number_characteristic_subgroups': None, 'number_conjugacy_classes': 75, 'number_divisions': 61, 'number_normal_subgroups': None, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1679616, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7047], [3, 6560], [4, 108216], [6, 38880], [8, 839808], [12, 259200], [16, 419904]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': None, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '8.5', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 8, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 4], [2, 4], [4, 5], [8, 4], [32, 4], [64, 10], [128, 6], [256, 24]], 'representations': {'PC': {'code': '649141643801403140991035964443765254050625767528151848756521076195164030459133442497458725659334500799266911730612361474284030064957543327510307336610879910243515973170640468410876836521308336436690306842495936544241417491343393355630088140257934314573443540221367159365542071174545685601062775471146942792787234263113309840030991543179667401716184393301110578150488499786746003351003650194190611401296999757379682047628295793795438523903882969515707159773416390221200523841214456930494348068066233872593043118908161457880614950170448550782145621606719578149422538349059462459426327947737208576655113491087099182620541183', 'gens': [1, 3, 5, 8, 10, 11, 12, 13, 14, 15, 16], 'pres': [16, -2, -2, -2, -2, 2, -2, -2, 2, -3, 3, 3, 3, 3, 3, 3, 3, 32, 2105873, 43417922, 2886450, 130, 3596803, 40675603, 12378163, 29761924, 59605140, 24932836, 11950932, 228, 5827589, 80549397, 31152421, 17667509, 277, 50011142, 93861398, 955174, 19558838, 27189255, 42393623, 28203047, 9672759, 8428615, 6695511, 529767, 375, 157704200, 72161304, 82984, 29698616, 8257608, 2685400, 1256, 222658569, 50872345, 16056361, 1469497, 9054793, 4992089, 3945, 1344121, 206491658, 121380890, 72596522, 6369850, 15172682, 2779482, 12778, 6458, 171245579, 36323355, 32944171, 8398907, 8991819, 141403, 41579, 1748859, 46964748, 168769564, 25758764, 15934524, 21096268, 5416412, 134892, 67516, 283680781, 13533213, 68210733, 32757821, 22919757, 11642717, 435565, 1137149, 387809294, 13670430, 66355246, 13708862, 21335118, 9688414, 1399790, 2514366, 318636047, 99713055, 72908847, 22126655, 6418511, 9070687, 4479087, 73855]}, 'Perm': {'d': 36, 'gens': [370499269349287506978852091461450846433629, 212139679869269128555810056572826433201481]}}, 'schur_multiplier': [3], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': None, 'subgroup_index_bound': None, 'supersolvable': False, 'sylow_subgroups_known': False, 'tex_name': 'C_3^8.C_4:\\OD_{16}.C_2^2', 'transitive_degree': None, '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': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 48, 'aut_gen_orders': None, 'aut_gens': [[117635899382695670896743841408361219088290, 41385768963436925426803053031375283665226, 21300737289660421092597957053252033099363, 31348116926917302048766235075067323693100], [169892903206436213370601759576862119908620, 33076072994754930527653441167648919823734, 1806928228556912663876426171367267098870, 62616217410280194855565130159644374413438], [370768698898620761773006499343523454790280, 255294427298622306276351395518448527984583, 21587780663367327018626985470200645240600, 938612381543215421184464761842058913270], [340080793413150880529555976021668213227305, 83846140135119008347003917706235027602590, 51710233877449115254444731098873749353609, 10976774490765740574439616348326811189600], [330034746123935881197576249957111636960856, 21587287036339589924225373051551893147916, 62329125761160580019421756689988778468995, 63197481925999922834395242152606643802030], [147445704886478166406124408623764943276241, 21301239404793886179848323231248847617499, 32789523248073306375852531137676299904638, 51710233877447101999417293488623229393562]], 'aut_group': '53747712.ks', 'aut_hash': 5836576575400874840, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 53747712, 'aut_permdeg': 95904, 'aut_perms': None, 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 648, 2, 1], [2, 1296, 1, 1], [2, 2592, 1, 1], [2, 6561, 1, 1], [3, 32, 1, 1], [3, 64, 1, 2], [3, 128, 2, 1], [3, 512, 2, 4], [3, 1024, 1, 2], [4, 324, 1, 1], [4, 648, 1, 1], [4, 5832, 1, 1], [4, 5832, 2, 1], [4, 13122, 1, 2], [4, 23328, 1, 2], [4, 23328, 4, 1], [4, 26244, 1, 2], [4, 52488, 1, 1], [4, 52488, 2, 1], [4, 104976, 1, 1], [4, 209952, 1, 1], [6, 2592, 1, 1], [6, 5184, 1, 3], [6, 10368, 1, 2], [6, 10368, 2, 2], [6, 20736, 1, 2], [6, 41472, 2, 4], [8, 13122, 1, 2], [8, 26244, 1, 3], [8, 26244, 2, 1], [8, 46656, 1, 1], [8, 52488, 1, 5], [8, 104976, 2, 1], [8, 104976, 4, 2], [8, 209952, 1, 1], [8, 419904, 1, 1], [12, 2592, 2, 1], [12, 5184, 2, 1], [12, 10368, 1, 2], [12, 20736, 2, 1], [12, 46656, 1, 1], [12, 46656, 2, 2], [12, 93312, 1, 1], [12, 93312, 2, 1], [12, 186624, 4, 1], [16, 209952, 8, 1], [24, 93312, 2, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_3^8:C_4^2.D_4^2:D_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': None, 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': None, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': 53747712, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 162, 1], [2, 324, 1], [2, 648, 2], [2, 1296, 1], [2, 2592, 1], [2, 6561, 1], [3, 32, 1], [3, 64, 2], [3, 128, 2], [3, 512, 8], [3, 1024, 2], [4, 324, 1], [4, 648, 1], [4, 5832, 3], [4, 13122, 2], [4, 23328, 6], [4, 26244, 2], [4, 52488, 3], [4, 104976, 1], [4, 209952, 1], [6, 2592, 1], [6, 5184, 3], [6, 10368, 6], [6, 20736, 2], [6, 41472, 8], [8, 13122, 2], [8, 26244, 5], [8, 46656, 1], [8, 52488, 5], [8, 104976, 10], [8, 209952, 1], [8, 419904, 1], [12, 2592, 2], [12, 5184, 2], [12, 10368, 2], [12, 20736, 2], [12, 46656, 5], [12, 93312, 3], [12, 186624, 4], [16, 209952, 8], [24, 93312, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': None, 'central_quotient': '6718464.bbw', 'commutator_count': 1, 'commutator_label': None, 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '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', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 18, 'conjugacy_classes_known': True, 'counter': 725, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': None, 'direct_product': None, 'div_stats': [[1, 1, 1, 1], [2, 162, 1, 1], [2, 324, 1, 1], [2, 648, 1, 2], [2, 1296, 1, 1], [2, 2592, 1, 1], [2, 6561, 1, 1], [3, 32, 1, 1], [3, 64, 1, 2], [3, 128, 1, 2], [3, 512, 1, 8], [3, 1024, 1, 2], [4, 324, 1, 1], [4, 648, 1, 1], [4, 5832, 1, 1], [4, 5832, 2, 1], [4, 13122, 1, 2], [4, 23328, 1, 6], [4, 26244, 1, 2], [4, 52488, 1, 3], [4, 104976, 1, 1], [4, 209952, 1, 1], [6, 2592, 1, 1], [6, 5184, 1, 3], [6, 10368, 1, 6], [6, 20736, 1, 2], [6, 41472, 1, 8], [8, 13122, 2, 1], [8, 26244, 1, 1], [8, 26244, 2, 2], [8, 46656, 1, 1], [8, 52488, 1, 3], [8, 52488, 2, 1], [8, 104976, 1, 2], [8, 104976, 2, 4], [8, 209952, 1, 1], [8, 419904, 1, 1], [12, 2592, 2, 1], [12, 5184, 2, 1], [12, 10368, 1, 2], [12, 20736, 1, 2], [12, 46656, 1, 1], [12, 46656, 2, 2], [12, 93312, 1, 3], [12, 186624, 1, 4], [16, 209952, 2, 4], [24, 93312, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 48, 'exponents_of_order': [10, 8], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[32, 0, 4], [32, 1, 4], [64, 0, 4], [64, 1, 14], [128, 0, 2], [128, 1, 11], [256, -1, 2], [512, 1, 16], [1024, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '6718464.bbw', 'hash': 5091201899506233364, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [16, 12, 8, 8], 'inner_gens': [[117635899382695670896743841408361219088290, 255294427298623036621620451368385223295975, 22169045179087132010619946365936015277272, 1225663712837555534467017287866140439249], [299625496460338886717042557233517717060905, 41385768963436925426803053031375283665226, 63197481925999115733209025763754005925479, 938612381545276502442993693455504364284], [168676448551228310263029154788026839690053, 31347064686513514854967107113822395925729, 21300737289660421092597957053252033099363, 22169045179089100051591676890641300024195], [117037515447711747086613086559388880116716, 10976535771738039642479542172144005703634, 32789523248072052395780221099879311091838, 31348116926917302048766235075067323693100]], 'inner_hash': 5091201899506233364, 'inner_nilpotent': False, 'inner_order': 6718464, 'inner_split': None, 'inner_tex': 'C_3^8:C_4^2.Q_{16}:C_2^2', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 32, 'irrQ_degree': 32, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 20], [4, 14], [8, 11], [32, 8], [64, 18], [128, 13], [256, 2], [512, 16], [1024, 2]], 'label': '6718464.bbw', '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': 'C3^8:C4^2.Q16:C2^2', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 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, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 9, 0, 0, 0, 15, 0, 0, 0, 23, 0, 0, 27, 0, 35, 0, 15, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 77, 'number_characteristic_subgroups': 58, 'number_conjugacy_classes': 120, 'number_divisions': 101, 'number_normal_subgroups': 136, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 6718464, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 12231], [3, 6560], [4, 709560], [6, 453600], [8, 2146176], [12, 1337472], [16, 1679616], [24, 373248]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '8.5', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 8, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^3', 'pc_rank': None, 'perfect': False, 'permutation_degree': 36, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 16], [2, 12], [4, 10], [8, 7], [16, 2], [32, 5], [64, 16], [128, 11], [256, 4], [512, 16], [1024, 2]], 'representations': {'PC': {'code': '363684519855727186920687131171428705088377058962746720762658457505216907640549625314287683516749894447815515203264858343203604054585081116220949421437420309903985745761588086527276656184666742549549902742840030839753598064881874023983269548275928658539969708281925389633644572181449600806249825479194255863335308891119965644854826612694415589604934276298203491404110273754961924263332841590487900429119562376739454870061301804306954264928153233002206799168064285705026442920992863814334812619732477580715883352333298389103733680721104924745589221675995376370760153404544509399842291244247520978930721860787955820609749662103765701081465918583819247010076617436340114807002148179034642519055764751420916587443613480865308782983772222986700924575587106546275332730181117290221225449747915372183469925947708209139019716285136300241716852568274322606574705574698768169289676281768221923559079286748941062504703', 'gens': [1, 2, 5, 6, 9, 12, 13, 14, 15, 16, 17, 18], 'pres': [18, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 71748864, 102138841, 91, 311462282, 146, 206448195, 40689849, 203041444, 287318182, 102220240, 64258798, 32619676, 518216837, 324278231, 139130825, 82474475, 8185397, 311, 634886790, 217635288, 55389642, 45127212, 35797686, 366, 768264199, 380224537, 212009515, 5402941, 13604047, 836946440, 309707738, 34494380, 14624126, 14595632, 26989298, 14692220, 6860186, 476, 628439049, 592646427, 189457965, 119174463, 38759121, 2070819, 15671637, 716535, 531, 843651082, 627720220, 322679854, 105481792, 73713106, 26376868, 17132662, 3304, 1042219019, 117780509, 60162095, 144930881, 38679635, 27731045, 13817207, 10505, 5344859, 2676413, 1024358412, 311261214, 346664496, 185193282, 83161812, 27159078, 23149272, 33834, 3386604, 8598, 632733709, 400877599, 385394737, 192052291, 13692757, 8846311, 4564345, 109003, 1596829, 2236423, 281733134, 310625312, 409605170, 34352708, 35493206, 37178024, 3663482, 350060, 4179758, 1603976, 1369571343, 211451937, 426000435, 51425349, 50430039, 14183529, 10368123, 1119885, 5090847, 280113, 869216272, 600523810, 314049076, 201441094, 35819224, 20896234, 3314716, 3569326, 3161752, 1421242, 96878609, 183140387, 368603189, 953927, 95240537, 54483947, 21684797, 11337551, 7546769, 1423187]}, 'Perm': {'d': 36, 'gens': [21300737289660421092597957053252033099363, 31348116926917302048766235075067323693100, 41385768963436925426803053031375283665226, 117635899382695670896743841408361219088290]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 24, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^8:C_4^2.Q_{16}:C_2^2', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_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, 3]], 'center_label': '4.2', 'center_order': 4, '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', '2.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', '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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
