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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '679477248.cl', 'ambient_counter': 64, 'ambient_order': 679477248, 'ambient_tex': 'C_2^9.(A_4^2\\wr C_2.C_2^2.D_4)', 'central': False, 'central_factor': False, 'centralizer_order': None, 'characteristic': False, 'core_order': 512, 'counter': 896, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '679477248.cl.1327104._.B', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '1327104.B', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '1327104.d', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': None, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1327104, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'A_4^2\\wr C_2.C_2^2.D_4', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '512.10494213', 'subgroup_hash': None, 'subgroup_order': 512, 'subgroup_tex': 'C_2^9', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '679477248.cl', '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': [357001369764481, 8683317618811912398747520558414833961, 39921961, 8222849558584435296148908510033846, 10888895302556736146153477166, 10333147966386160440927907255781302272000, 1313901393846, 8852666374451254581175978833846, 6267305646], 'label': '679477248.cl.1327104._.B', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '1327104.B', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '1327104._.B', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '512.10494213', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 0, 'aut_exponent': 24624517680, 'aut_gen_orders': [2, 9], 'aut_gens': [[1, 2, 4, 8, 16, 32, 64, 128, 256], [3, 2, 4, 8, 16, 32, 64, 128, 256], [256, 1, 2, 4, 8, 16, 32, 64, 128]], 'aut_group': None, 'aut_hash': 3475559796451453123, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 699612310033197642547200, 'aut_permdeg': 511, 'aut_perms': [1329076649454784293232248790960488187618561193564925218031901523314975154529473956940420952253844366423978751423927126247076050127336432360744865853718082268482031259757922292929237842936999486432987316818686408739072677074403800929685525647864973396898530364501473510597117621803991726186749860878524704290262705249932695244466526132364600401798521151415015038001286207153354390081319867530635341924049179087287563167341200591662666928415813077812212321054010761042273106599133015383829033754630111258493885629483424318179881784448931366594602302095402012352490356683852911724588229431649120881754182120349985967313465980975720152778314679815971451751705250055271764253860631449157385418935219547285308406482410974137014089035616642561144796456493500989736313844340588895225885205617209294210565638760728636501894662672934505783152285472888670085700094873230265730044326257198638321439247977211694333743392716971813516561055251468403694283989757018016992289013431151649192433009216538344717081735199177885256136451241079574638807091310732220984435364827027594133935075814536440092897563524629010769461483354436959728786592208862146318479640410018435296633194880, 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'aut_phi_ratio': 2.7328605860671783e+21, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 511, 1]], 'aut_supersolvable': False, 'aut_tex': '\\GL(9,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24624517680, 'autcent_group': None, 'autcent_hash': 3475559796451453123, 'autcent_nilpotent': False, 'autcent_order': 699612310033197642547200, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': '\\GL(9,2)', '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, 511]], 'center_label': '512.10494213', 'center_order': 512, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, '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'], 'composition_length': 9, 'conjugacy_classes_known': False, 'counter': 10494213, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 9]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 511]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [9], 'factors_of_aut_order': [2, 3, 5, 7, 17, 31, 73, 127], 'factors_of_order': [2], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '512.10494213', 'hash': 10494213, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'inner_gens': [[1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256], [1, 2, 4, 8, 16, 32, 64, 128, 256]], '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': None, 'irrep_stats': [[1, 512]], 'label': '512.10494213', 'linC_count': None, 'linC_degree': 9, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': None, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^9', 'ngens': 9, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 2, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 512, 'number_divisions': 512, 'number_normal_subgroups': 8283458, 'number_subgroup_autclasses': 10, 'number_subgroup_classes': 8283458, 'number_subgroups': 8283458, 'old_label': None, 'order': 512, 'order_factorization_type': 7, 'order_stats': [[1, 1], [2, 511]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24624517680, 'outer_gen_orders': [2, 9], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2, 4, 8, 16, 32, 64, 128, 256], [256, 1, 2, 4, 8, 16, 32, 64, 128]], 'outer_group': None, 'outer_hash': 3475559796451453123, 'outer_nilpotent': False, 'outer_order': 699612310033197642547200, 'outer_permdeg': 511, 'outer_perms': [1329076649454784293232248790960488187618561193564925218031901523314975154529473956940420952253844366423978751423927126247076050127336432360744865853718082268482031259757922292929237842936999486432987316818686408739072677074403800929685525647864973396898530364501473510597117621803991726186749860878524704290262705249932695244466526132364600401798521151415015038001286207153354390081319867530635341924049179087287563167341200591662666928415813077812212321054010761042273106599133015383829033754630111258493885629483424318179881784448931366594602302095402012352490356683852911724588229431649120881754182120349985967313465980975720152778314679815971451751705250055271764253860631449157385418935219547285308406482410974137014089035616642561144796456493500989736313844340588895225885205617209294210565638760728636501894662672934505783152285472888670085700094873230265730044326257198638321439247977211694333743392716971813516561055251468403694283989757018016992289013431151649192433009216538344717081735199177885256136451241079574638807091310732220984435364827027594133935075814536440092897563524629010769461483354436959728786592208862146318479640410018435296633194880, 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'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': '\\GL(9,2)', 'pc_rank': None, 'perfect': False, 'permutation_degree': 18, 'pgroup': 2, 'primary_abelian_invariants': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 9, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 512]], 'representations': {'PC': {'code': '0', 'gens': [1, 2, 3, 4, 5, 6, 7, 8, 9], 'pres': [9, -2, 2, 2, 2, 2, 2, 2, 2, 2]}, 'Perm': {'d': 18, 'gens': [355687428096000, 1307674368000, 6227020800, 39916800, 362880, 5040, 120, 6, 1]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^9', 'transitive_degree': 512, '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': '16.10', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[308151428397909399030493231489112785481815, 180405150131754582660457869545722951390679, 276624407170631188039297504953431177025847], [212836187003233842757993196120928037529039, 170072002165368453241950292230909276197161, 234119558627831033880157877332877108249033], [223169334969619987687659723948452287446070, 180405150131754582660457867267760774926056, 371957447883460094753165283327508136961232], [350638375217868355605228501202308591976614, 180387308191204751014067165461477316926662, 319066366849290405041030114738128842965758], [308151428397909399030493231489112785481815, 180405150131754582660457869545722951390679, 276624407170631188039297504953431177025847], [286930435684619213394313066392494491130743, 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[24, 1769472, 1, 12]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 48, 'exponents_of_order': [23, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[18, 1, 8], [36, 1, 22], [72, 0, 4], [72, 1, 40], [81, 0, 8], [108, 1, 32], [144, 1, 30], [162, 0, 4], [162, 1, 26], [216, 1, 56], [288, 1, 22], [324, 0, 16], [324, 1, 68], [432, 1, 60], [648, 0, 20], [648, 1, 84], [864, 1, 20], [1296, 0, 16], [1296, 1, 54], [2592, 1, 20]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '339738624.gt', 'hash': 998912746418625114, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': None, 'inner_split': None, 'inner_tex': 'C_2^{16}.C_3^4.D_4:D_4', 'inner_used': None, 'irrC_degree': 18, 'irrQ_degree': 18, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 16], [2, 12], 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646088156, 323037665, 116996048, 58288247, 19499642, 9715031]}, 'Perm': {'d': 36, 'gens': [308151428397909399030493231489112785481815, 180405150131754582660457869545722951390679, 276624407170631188039297504953431177025847]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^9.(A_4^2\\wr C_2.C_2^2.D_4)', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
-
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 48, 'aut_gen_orders': [8, 24, 24], 'aut_gens': [[20829344644064, 5693540049228, 3929601745418], [5786821997154, 18133000742868, 13828073823500], [9616479707389, 18213948370791, 1488736971945], [5606321846396, 18213908459016, 1395331654198]], 'aut_group': '2654208.a', 'aut_hash': 3325821346044436304, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 2654208, 'aut_permdeg': 1440, 'aut_perms': 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'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 12, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [2, 72, 1, 1], [2, 81, 1, 1], [2, 108, 1, 1], [2, 144, 1, 1], [2, 432, 1, 1], [2, 576, 1, 2], [2, 576, 2, 1], [2, 648, 1, 1], [2, 864, 1, 1], [2, 1296, 1, 2], [2, 1728, 1, 1], [3, 32, 1, 1], [3, 128, 1, 1], [3, 256, 1, 1], [3, 2048, 1, 1], [3, 4096, 1, 1], [4, 72, 1, 1], [4, 144, 1, 2], [4, 288, 1, 2], [4, 432, 1, 1], [4, 576, 1, 1], [4, 648, 1, 1], [4, 864, 1, 4], [4, 1296, 1, 3], [4, 1728, 1, 4], [4, 2592, 1, 3], [4, 3456, 1, 1], [4, 3456, 2, 1], [4, 5184, 1, 6], [4, 5184, 2, 1], [4, 10368, 1, 2], [4, 10368, 2, 1], [4, 20736, 1, 1], [4, 20736, 2, 1], [6, 96, 1, 1], [6, 192, 1, 1], [6, 288, 1, 1], [6, 576, 1, 1], [6, 768, 1, 1], [6, 864, 1, 1], [6, 1152, 1, 2], [6, 1536, 1, 1], [6, 2304, 1, 2], [6, 3456, 1, 1], [6, 4608, 1, 3], [6, 6144, 1, 1], [6, 6912, 1, 1], [6, 9216, 1, 2], [6, 9216, 2, 1], [6, 13824, 1, 1], [6, 36864, 1, 2], [6, 36864, 2, 1], [8, 288, 1, 1], [8, 1728, 1, 1], [8, 2592, 1, 1], [8, 10368, 1, 2], [8, 10368, 2, 1], [8, 20736, 1, 1], [8, 20736, 2, 2], [8, 41472, 2, 1], [8, 82944, 2, 1], [12, 1152, 1, 1], [12, 2304, 1, 4], [12, 3456, 1, 1], [12, 4608, 1, 4], [12, 6912, 1, 4], [12, 9216, 1, 2], [12, 13824, 1, 4], [12, 18432, 1, 2], [12, 27648, 1, 1], [12, 27648, 2, 1], [12, 36864, 1, 1], [16, 82944, 2, 1], [24, 4608, 1, 1], [24, 13824, 1, 1], [24, 18432, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^8.S_3\\wr 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': '2654208.a', 'autcentquo_hash': 3325821346044436304, 'autcentquo_nilpotent': False, 'autcentquo_order': 2654208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^8.S_3\\wr D_4', 'cc_stats': [[1, 1, 1], [2, 12, 1], [2, 18, 1], [2, 36, 1], [2, 72, 1], [2, 81, 1], [2, 108, 1], [2, 144, 1], [2, 432, 1], [2, 576, 4], [2, 648, 1], [2, 864, 1], [2, 1296, 2], [2, 1728, 1], [3, 32, 1], [3, 128, 1], [3, 256, 1], [3, 2048, 1], [3, 4096, 1], [4, 72, 1], [4, 144, 2], [4, 288, 2], [4, 432, 1], [4, 576, 1], [4, 648, 1], [4, 864, 4], [4, 1296, 3], [4, 1728, 4], [4, 2592, 3], [4, 3456, 3], [4, 5184, 8], [4, 10368, 4], [4, 20736, 3], [6, 96, 1], [6, 192, 1], [6, 288, 1], [6, 576, 1], [6, 768, 1], [6, 864, 1], [6, 1152, 2], [6, 1536, 1], [6, 2304, 2], [6, 3456, 1], [6, 4608, 3], [6, 6144, 1], [6, 6912, 1], [6, 9216, 4], [6, 13824, 1], [6, 36864, 4], [8, 288, 1], [8, 1728, 1], [8, 2592, 1], [8, 10368, 4], [8, 20736, 5], [8, 41472, 2], [8, 82944, 2], [12, 1152, 1], [12, 2304, 4], [12, 3456, 1], [12, 4608, 4], [12, 6912, 4], [12, 9216, 2], [12, 13824, 4], [12, 18432, 2], [12, 27648, 3], [12, 36864, 1], [16, 82944, 2], [24, 4608, 1], [24, 13824, 1], [24, 18432, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '1327104.d', 'commutator_count': 1, 'commutator_label': '165888.bl', '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', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 18, 'conjugacy_classes_known': True, 'counter': 4, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 12, 1, 1], [2, 18, 1, 1], [2, 36, 1, 1], [2, 72, 1, 1], [2, 81, 1, 1], [2, 108, 1, 1], [2, 144, 1, 1], [2, 432, 1, 1], [2, 576, 1, 4], [2, 648, 1, 1], [2, 864, 1, 1], [2, 1296, 1, 2], [2, 1728, 1, 1], [3, 32, 1, 1], [3, 128, 1, 1], [3, 256, 1, 1], [3, 2048, 1, 1], [3, 4096, 1, 1], [4, 72, 1, 1], [4, 144, 1, 2], [4, 288, 1, 2], [4, 432, 1, 1], [4, 576, 1, 1], [4, 648, 1, 1], [4, 864, 1, 4], [4, 1296, 1, 3], [4, 1728, 1, 4], [4, 2592, 1, 3], [4, 3456, 1, 3], [4, 5184, 1, 8], [4, 10368, 1, 4], [4, 20736, 1, 3], [6, 96, 1, 1], [6, 192, 1, 1], [6, 288, 1, 1], [6, 576, 1, 1], [6, 768, 1, 1], [6, 864, 1, 1], [6, 1152, 1, 2], [6, 1536, 1, 1], [6, 2304, 1, 2], [6, 3456, 1, 1], [6, 4608, 1, 3], [6, 6144, 1, 1], [6, 6912, 1, 1], [6, 9216, 1, 4], [6, 13824, 1, 1], [6, 36864, 1, 4], [8, 288, 1, 1], [8, 1728, 1, 1], [8, 2592, 1, 1], [8, 10368, 1, 4], [8, 20736, 1, 5], [8, 41472, 1, 2], [8, 82944, 1, 2], [12, 1152, 1, 1], [12, 2304, 1, 4], [12, 3456, 1, 1], [12, 4608, 1, 4], [12, 6912, 1, 4], [12, 9216, 1, 2], [12, 13824, 1, 4], [12, 18432, 1, 2], [12, 27648, 1, 3], [12, 36864, 1, 1], [16, 82944, 1, 2], [24, 4608, 1, 1], [24, 13824, 1, 1], [24, 18432, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 48, 'exponents_of_order': [14, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 8], [18, 1, 8], [24, 1, 6], [36, 1, 14], [48, 1, 9], [72, 1, 10], [81, 1, 8], [96, 1, 4], [108, 1, 8], [144, 1, 10], [162, 1, 6], [216, 1, 6], [324, 1, 2], [432, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '1327104.d', 'hash': 4116506670747618155, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 48, 'inner_gen_orders': [12, 6, 12], 'inner_gens': [[20829344644064, 9703661617436, 15316372083604], [18133084195076, 5693540049228, 12694799578451], [8308769402749, 19615075601625, 3929601745418]], 'inner_hash': 4116506670747618155, 'inner_nilpotent': False, 'inner_order': 1327104, 'inner_split': True, 'inner_tex': 'A_4^2\\wr C_2.C_2^2.D_4', 'inner_used': [1, 2, 3], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 8], [2, 6], [4, 2], [8, 8], [12, 8], [16, 10], [18, 8], [24, 6], [32, 2], [36, 14], [48, 9], [72, 10], [81, 8], [96, 4], [108, 8], [144, 10], [162, 6], [216, 6], [324, 2], [432, 1]], 'label': '1327104.d', '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': 'A4^2wrC2.C2^2.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, 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': 122, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 136, 'number_divisions': 136, 'number_normal_subgroups': 29, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 1327104, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 9039], [3, 6560], [4, 180144], [6, 239712], [8, 398592], [12, 290304], [16, 165888], [24, 36864]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[20829384560744, 5693540049354, 3929601744578]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': None, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': False, 'ratrep_stats': [[1, 8], [2, 6], [4, 2], [8, 8], [12, 8], [16, 10], [18, 8], [24, 6], [32, 2], [36, 14], [48, 9], [72, 10], [81, 8], [96, 4], [108, 8], [144, 10], [162, 6], [216, 6], [324, 2], [432, 1]], 'representations': {'PC': {'code': '4327903453365276281223549395627500844469822304182829179758841984496775694886808247845708693714905302219697147108103863012913241888434290395518908194594278863506752073343071729433614507355202182181134788393972616600453961070675129090302665778244232495547846422577854572916450174963625159779489592220902015302607919508380935498695311064167585977638249840198000273178113861820918531230160906587096445216956483468313760219413207151492843478620600873317562826052737145501407052471652071716105463457429167647602088275832197283848839202596662590355928298162076328470614797964141193500702161782413808417420155115960122388412170525462882121741849391151210474021972839307300562581176718283117188979131717296031068656674095885127681228699091087623712753552548325225617051006889700889920', 'gens': [1, 2, 4, 5, 7, 9, 11, 13, 14, 15, 16, 17, 18], 'pres': [18, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 2, 8572032, 8119801, 91, 51028490, 8716610, 48377091, 46583445, 20498295, 29636644, 28271182, 27876820, 14522638, 256, 86410373, 22871831, 18890537, 15350747, 131799030, 54057552, 25811898, 7620, 3578226, 4198542, 366, 8128519, 5557273, 40623019, 6973, 19087, 47617, 6505928, 77563034, 12923756, 8654750, 2181248, 2364974, 1947032, 360746, 476, 223061769, 65044827, 1658925, 414801, 4088979, 82197, 136863946, 123190876, 3392974, 2951056, 1090666, 5100184, 573922, 369010, 586, 280696331, 41501, 68802095, 8491475, 3965861, 1617527, 24261132, 41243934, 40030896, 10614324, 4700694, 1516440, 43716, 21270, 107122189, 53561119, 40497457, 326677, 5715463, 1905241, 299533, 158935, 53113, 25159, 145566734, 53187872, 74882930, 14696708, 19420646, 2449544, 583322, 466700, 42314, 22082, 8957967, 150792225, 14307891, 18662469, 8802519, 7278441, 3172731, 777741, 445983, 212721, 93507, 36501, 171320848, 152285218, 52480276, 13913296, 2181274, 1784716, 694150, 25900, 13984, 118133009, 57386915, 25614233, 6088715, 4409117, 396737, 17675, 56573, 59507]}, 'Perm': {'d': 16, 'gens': [20829344644064, 3929601745418, 5693540049228]}}, 'schur_multiplier': [2, 2, 2, 2], 'semidirect_product': None, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 256, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_4^2\\wr C_2.C_2^2.D_4', 'transitive_degree': 16, 'wreath_data': None, 'wreath_product': False}
