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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '5832.he', 'ambient_counter': 187, 'ambient_order': 5832, 'ambient_tex': '\\He_3^2:C_2^3', 'central': False, 'central_factor': False, 'centralizer_order': 2916, 'characteristic': True, 'core_order': 3, 'counter': 313, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '5832.he.1944.b1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '1944.b1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '1944.3723', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3723, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 1944, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2\\times C_3^3:S_3^2', 'simple': True, 'solvable': True, 'special_labels': ['C8', 'C8'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '3.1', 'subgroup_hash': 1, 'subgroup_order': 3, 'subgroup_tex': 'C_3', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '5832.he', 'aut_centralizer_order': None, 'aut_label': '1944.b1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.b1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['648.a1', '648.e1', '648.f1', '648.g1', '972.b1', '972.j1', '972.m1'], 'contains': ['5832.a1'], 'core': '1944.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [5769, 4404, 4739, 7711], 'generators': [801966403472517528], 'label': '5832.he.1944.b1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '1944.b1', 'normal_contained_in': ['648.a1', '972.b1'], 'normal_contains': ['5832.a1'], 'normalizer': '1.a1', 'old_label': '1944.b1', 'projective_image': '5832.he', 'quotient_action_image': '2.1', 'quotient_action_kernel': '972.864', 'quotient_action_kernel_order': 972, 'quotient_fusion': None, 'short_label': '1944.b1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [2]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 2, 'autcent_group': '2.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 2, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_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], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, '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': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 3]], 'label': '3.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3', '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': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], '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': 1, 'perfect': False, 'permutation_degree': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, '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': 6, 'aut_exponent': 72, 'aut_gen_orders': [18, 12, 8, 8, 6], 'aut_gens': [[378918547503936751, 141989159861304486, 270414615046451184], [423050652587702430, 634455485283758647, 2039533249841554734], [381665277724047409, 914562325859349007, 1422975722592953185], [1461297602838140911, 653409774971874271, 1240503756195298687], [1156394210848622304, 702527163034925929, 525209604249867150], [854295271084056264, 1657447241782053001, 1410044817670211928]], 'aut_group': None, 'aut_hash': 1709489304420586638, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 186624, 'aut_permdeg': 108, 'aut_perms': [707281688450806025248818299764727418656387459430807262717814481776542869499554893197629557397300358406221579731102341251635890629790805448937177640244673526613691551632440923, 81033311540560268453689318619084455535238728823900343476385214955144704283117258710483518209302104987171454388371777286581578934203179021548401313005835412190036451205024299, 738557700166580026425078985279106520105867308568945008522306002674576885195586264727965056399317776427235734208058407886971894129515110000727667187698800007911601915604758316, 639570190770060686226327940894765287197882361850870715118710217709885701683837931912331419925479121629308457129287815244656240243968217927155078306183111666865855323499689156, 156587278970772071527132764861998373746986382840529590962118710117222598959967905496172655904910504359361083966290316378069699856093135713943193673534032966099511719338642070], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 4, 1], [2, 81, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 12, 4, 1], [3, 12, 8, 1], [3, 18, 8, 1], [3, 36, 12, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 12, 4, 1], [6, 12, 8, 1], [6, 18, 8, 1], [6, 27, 8, 1], [6, 36, 12, 1], [6, 81, 4, 1], [6, 162, 2, 1], [6, 162, 4, 1], [6, 162, 16, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^3:C_3^2.Q_8.D_6.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 72, 'autcentquo_group': '46656.jt', 'autcentquo_hash': 7932973419676711738, 'autcentquo_nilpotent': False, 'autcentquo_order': 46656, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:\\SOPlus(4,2).S_4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 27, 4], [2, 81, 2], [3, 1, 2], [3, 2, 3], [3, 12, 12], [3, 18, 8], [3, 36, 12], [6, 1, 2], [6, 2, 3], [6, 12, 12], [6, 18, 8], [6, 27, 8], [6, 36, 12], [6, 81, 4], [6, 162, 22]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '972.811', 'commutator_count': 1, 'commutator_label': '729.453', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 187, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['2916.eo', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 27, 1, 4], [2, 81, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 12, 1, 4], [3, 12, 2, 4], [3, 18, 1, 8], [3, 36, 1, 12], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 12, 1, 4], [6, 12, 2, 4], [6, 18, 1, 8], [6, 27, 2, 4], [6, 36, 1, 12], [6, 81, 2, 2], [6, 162, 1, 18], [6, 162, 2, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 122472, 'exponent': 6, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 4], [12, 0, 8]], 'familial': False, 'frattini_label': '9.2', 'frattini_quotient': '648.750', 'hash': 2107098625061990260, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [6, 6, 6], 'inner_gens': [[378918547503936751, 168989850521747694, 558878208142928808], [895354849751122921, 141989159861304486, 766770173272522254], [1680200001134944135, 1653642507952528110, 270414615046451184]], 'inner_hash': 811, 'inner_nilpotent': False, 'inner_order': 972, 'inner_split': False, 'inner_tex': 'C_3^3:S_3^2', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 32], [4, 32], [6, 8], [9, 16], [12, 16], [18, 4]], 'label': '5832.he', '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': 'He3^2:C2^3', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 116, 'number_divisions': 96, 'number_normal_subgroups': 122, 'number_subgroup_autclasses': 322, 'number_subgroup_classes': 2997, 'number_subgroups': 62866, 'old_label': None, 'order': 5832, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 271], [3, 728], [6, 4832]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 3, 2, 2], 'outer_gen_pows': [0, 809497817483122920, 0, 0, 809497817483122920, 809497817483122920, 809497817483122920], 'outer_gens': [[383351300912104609, 223210132406961840, 349181238300506784], [432789241461359046, 857149924509226201, 1965765165610242294], [378918547503936750, 141989159861304486, 270414615046451185], [378918547503936750, 141989159861304487, 270414615046451184], [891757166416663951, 899974246414579926, 537909999718465590], [1743274226090154511, 1797387457704313104, 2052462924219678504], [2136356450098154065, 387868883365598430, 804030427318260366]], 'outer_group': '192.1472', 'outer_hash': 1472, 'outer_nilpotent': False, 'outer_order': 192, 'outer_permdeg': 8, 'outer_perms': [120, 1, 16, 7, 1440, 16680, 11520], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'D_4\\times S_4', 'pc_rank': None, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 32], [4, 32], [12, 4], [18, 12], [24, 8]], 'representations': {'PC': {'code': '1904564378722777943222732726036483206841846452800137235558172834311642196068727585107127169655379551', 'gens': [1, 2, 4, 6, 7, 8, 9], 'pres': [9, -2, -2, -3, -2, -3, -3, -3, -3, -3, 9288, 42085, 46, 87698, 36723, 91812, 46785, 102, 52924, 67513, 29452, 241061, 130262, 27239, 23684, 6035, 299382, 13623, 28383, 7413, 807, 93319, 46672]}, 'Perm': {'d': 20, 'gens': [378918547503936751, 141989159861304486, 270414615046451184]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '\\He_3^2:C_2^3', 'transitive_degree': 36, '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': 5, 'aut_exponent': 24, 'aut_gen_orders': [8, 12, 6], 'aut_gens': [[24577758, 26172358, 2939606, 1017496, 25633100, 28816400, 6810638, 13886268], [14408275, 18902522, 37043650, 27520034, 30711386, 28816400, 35429959, 38037303], [11495116, 27247603, 14408242, 6560276, 25945430, 28816400, 27247595, 39306232], [35376706, 27848050, 13111867, 15502983, 14198556, 28816400, 32864335, 42236362]], 'aut_group': '746496.y', 'aut_hash': 7567673007815161820, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 746496, 'aut_permdeg': 36, 'aut_perms': [279469978983289796492939259408672734572100, 204513563301881865418501211154399384581051, 46097658467693552821258182941854329973241], 'aut_phi_ratio': 1152.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 4, 1], [2, 81, 2, 1], [3, 1, 2, 1], [3, 6, 8, 1], [3, 12, 16, 1], [6, 1, 2, 1], [6, 6, 8, 1], [6, 9, 8, 1], [6, 12, 16, 1], [6, 54, 16, 1], [6, 81, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2:S_3^2.\\POPlus(4,3)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '186624.d', 'autcentquo_hash': 632540685664682195, 'autcentquo_nilpotent': False, 'autcentquo_order': 186624, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(Q_8^2:S_3^2)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 9, 4], [2, 81, 2], [3, 1, 2], [3, 6, 8], [3, 12, 16], [6, 1, 2], [6, 6, 8], [6, 9, 8], [6, 12, 16], [6, 54, 16], [6, 81, 4]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '324.169', 'commutator_count': 1, 'commutator_label': '243.65', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 3723, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['972.812', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 9, 1, 4], [2, 81, 1, 2], [3, 1, 2, 1], [3, 6, 1, 8], [3, 12, 1, 16], [6, 1, 2, 1], [6, 6, 1, 8], [6, 9, 2, 4], [6, 12, 1, 16], [6, 54, 1, 16], [6, 81, 2, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 1134, 'exponent': 6, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[9, 0, 8]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '648.750', 'hash': 3723, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [3, 2, 3, 3, 3, 1, 2, 3], 'inner_gens': [[24577758, 13089749, 2939606, 1017496, 25633100, 28816400, 6810638, 34888062], [43014227, 26172358, 32864349, 15714108, 8092874, 28816400, 6810638, 21276652], [24577758, 39825765, 2939606, 1017496, 25633100, 28816400, 6810638, 17389827], [24577758, 41400411, 2939606, 1017496, 8194004, 28816400, 5236001, 34888062], [24577758, 29363677, 2939606, 23121499, 25633100, 28816400, 32325881, 13886268], [24577758, 26172358, 2939606, 1017496, 25633100, 28816400, 6810638, 13886268], [24577758, 26172358, 2939606, 2651191, 8092874, 28816400, 6810638, 17077587], [7138662, 33821261, 20201582, 23121499, 25633100, 28816400, 24350864, 13886268]], 'inner_hash': 169, 'inner_nilpotent': False, 'inner_order': 324, 'inner_split': False, 'inner_tex': 'C_3^2:S_3^2', 'inner_used': [1, 2, 4, 5, 7, 8], 'irrC_degree': 9, 'irrQ_degree': 18, 'irrQ_dim': 18, 'irrR_degree': 18, 'irrep_stats': [[1, 8], [2, 32], [4, 32], [9, 16]], 'label': '1944.3723', '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': 'C2*C3^3:S3^2', '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, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 13, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 88, 'number_divisions': 80, 'number_normal_subgroups': 118, 'number_subgroup_autclasses': 108, 'number_subgroup_classes': 1556, 'number_subgroups': 20360, 'old_label': None, 'order': 1944, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 199], [3, 242], [6, 1502]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 3, 2, 2], 'outer_gen_pows': [6810638, 14408200, 14408200, 26172358], 'outer_gens': [[24577758, 37798241, 2939606, 21766054, 30450095, 28816400, 6810638, 37818117], [24577758, 26172358, 2939606, 1017496, 4985672, 28816400, 6810638, 38037345], [20201582, 8733253, 32864349, 15714108, 25633100, 28816400, 24131645, 39087094], [35469088, 8733253, 16041895, 2651191, 8405129, 28816400, 7138687, 30492134]], 'outer_group': '2304.eo', 'outer_hash': 3879030643117341003, 'outer_nilpotent': False, 'outer_order': 2304, 'outer_permdeg': 12, 'outer_perms': [283455480, 48269640, 8356341, 383745103], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\wr S_3^2', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 32], [4, 32], [18, 8]], 'representations': {'PC': {'code': 3502206677795040031353915130061331863159901, 'gens': [1, 2, 3, 5, 6, 7], 'pres': [8, -2, -3, -2, -3, -3, -3, -2, -3, 65, 722, 7858, 66, 771, 20939, 500, 12117, 1045, 166]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [24577758, 26172358, 2939606, 1017496, 25633100, 28816400, 6810638, 13886268]}, 'Perm': {'d': 29, 'gens': [57702994498484394748609803174, 178123342089045174181340785, 1, 363043103102710208943971134374, 656703788598678026566518006294, 984207644064370820534597485446, 1300281433243500790941676685664, 1613762317596390570972647691960]}}, 'schur_multiplier': [2, 2, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 10, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_3^3:S_3^2', 'transitive_degree': 54, 'wreath_data': None, 'wreath_product': False}
