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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '62208.g', 'ambient_counter': 7, 'ambient_order': 62208, 'ambient_tex': 'C_6^4:(C_2\\times S_4)', 'central': False, 'central_factor': False, 'centralizer_order': 2, 'characteristic': False, 'core_order': 1296, 'counter': 36, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '62208.g.6.R', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '6.r1', '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': 6, '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': '10368.dh', 'subgroup_hash': 2306039712164322987, 'subgroup_order': 10368, 'subgroup_tex': 'C_6^3.(S_3\\times D_4)', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '62208.g', 'aut_centralizer_order': None, 'aut_label': '6.R', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '31104.A', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': ['3.A'], 'contains': ['12.BQ', '12.BT', '12.BU', '12.BX', '12.BY', '12.CH', '12.CI', '18.Y', '18.Z', '54.BE'], 'core': '48.B', 'coset_action_label': None, 'count': 3, 'diagramx': [4973, -1, 3993, -1], 'generators': [712682530576024, 3629527, 33479166347853338, 26064, 512629449402556081, 160834880721741271, 891796177002952230, 1110215538432000, 81, 79940904, 102270], 'label': '62208.g.6.R', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '3.A', 'old_label': '6.r1', 'projective_image': '31104.ji', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '6.R', '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [12, 4, 12, 12, 12, 12, 4, 4], 'aut_gens': [[1, 2, 24, 288, 3456], [8273, 1371, 7712, 5616, 3456], [5497, 7971, 304, 5976, 2304], [8001, 3755, 2176, 9864, 1152], [425, 4226, 4416, 4824, 1152], [8385, 8642, 6096, 7560, 2304], [7281, 4175, 7360, 9864, 2304], [5689, 3231, 5632, 8856, 1152], [1777, 2067, 3688, 3168, 3456]], 'aut_group': '20000.bi', 'aut_hash': 8564989553364120192, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 331776, 'aut_permdeg': 312, 'aut_perms': 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1], [6, 4, 1, 5], [6, 4, 2, 2], [6, 8, 1, 1], [6, 8, 2, 9], [6, 8, 4, 1], [6, 16, 1, 3], [6, 16, 2, 3], [6, 16, 4, 3], [6, 48, 1, 1], [6, 48, 2, 2], [6, 48, 4, 2], [6, 72, 2, 1], [6, 144, 1, 3], [6, 432, 1, 1], [12, 24, 2, 1], [12, 24, 4, 2], [12, 48, 4, 2], [12, 72, 2, 3], [12, 144, 1, 1], [12, 144, 4, 2], [12, 144, 8, 1], [12, 216, 2, 1], [12, 432, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_5^4:Q_{16}:C_2', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': None, 'autcentquo_hash': 172823512362682900, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.C_2^5.C_2^4', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 4, 1], [2, 24, 1], [2, 36, 2], [2, 81, 2], [2, 162, 1], [2, 216, 1], [2, 324, 1], [3, 2, 2], [3, 4, 3], [3, 8, 6], [3, 16, 1], [4, 12, 2], [4, 36, 2], [4, 72, 4], [4, 108, 2], [4, 216, 4], [6, 2, 2], [6, 4, 9], [6, 8, 23], [6, 16, 21], [6, 48, 13], [6, 72, 2], [6, 144, 3], [6, 432, 1], [12, 24, 10], [12, 48, 8], [12, 72, 6], [12, 144, 17], [12, 216, 2], [12, 432, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': None, 'commutator_count': 1, 'commutator_label': '648.687', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 11, 'conjugacy_classes_known': True, 'counter': 86, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 4, 1, 1], [2, 24, 1, 1], [2, 36, 1, 2], [2, 81, 1, 2], [2, 162, 1, 1], [2, 216, 1, 1], [2, 324, 1, 1], [3, 2, 1, 2], [3, 4, 1, 3], [3, 8, 1, 6], [3, 16, 1, 1], [4, 12, 1, 2], [4, 36, 1, 2], [4, 72, 2, 2], [4, 108, 1, 2], [4, 216, 2, 2], [6, 2, 1, 2], [6, 4, 1, 9], [6, 8, 1, 23], [6, 16, 1, 21], [6, 48, 1, 13], [6, 72, 1, 2], [6, 144, 1, 3], [6, 432, 1, 1], [12, 24, 1, 10], [12, 48, 1, 8], [12, 72, 1, 6], [12, 144, 1, 1], [12, 144, 2, 8], [12, 216, 1, 2], [12, 432, 2, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 860160, 'exponent': 12, 'exponents_of_order': [7, 4], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 6]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '1296.3528', 'hash': 2306039712164322987, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 12, 12, 12, 3], 'inner_gens': [[1, 10210, 264, 8928, 6912], [2777, 2, 6240, 3528, 1152], [49, 4442, 24, 1440, 3456], [5185, 3962, 2328, 288, 6912], [6913, 5762, 24, 7200, 3456]], 'inner_hash': 4181401253521402272, 'inner_nilpotent': False, 'inner_order': 5184, 'inner_split': None, 'inner_tex': 'C_3^4.C_2^3.C_2^3', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 16], [2, 20], [4, 34], [8, 68], [16, 21]], 'label': '10368.dh', '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': 'C6^3.(S3*D4)', 'ngens': 11, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 77, 'number_characteristic_subgroups': 55, 'number_conjugacy_classes': 159, 'number_divisions': 145, 'number_normal_subgroups': 99, 'number_subgroup_autclasses': 2961, 'number_subgroup_classes': 7153, 'number_subgroups': 305312, 'old_label': None, 'order': 10368, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 967], [3, 80], [4, 1464], [6, 2192], [12, 5664]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 4], 'outer_gen_pows': [3456, 192, 2976, 7193, 2304], 'outer_gens': [[3601, 4462, 1992, 5040, 3456], [193, 5738, 1752, 7344, 6912], [1969, 2774, 2904, 9072, 6912], [4345, 3767, 6776, 7704, 1152], [5961, 10295, 5272, 5616, 6912]], 'outer_group': '64.261', 'outer_hash': 261, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 32, 'outer_perms': [38378742594115524206056107685462583, 110420779799816455790728984786676394, 233306836329501706920963858351727776, 237091132333370412653725646943148656, 144610005871130851138627370823111176], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times C_2^3', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 34], [8, 62], [16, 25]], 'representations': {'PC': {'code': '2079050407758014480583833667949348320049665172506301647639661603986442562494789928127290341535560483309876732161887005400514114421108883', 'gens': [1, 2, 5, 8, 11], 'pres': [11, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 3, 224621, 56, 43430, 90, 102083, 14524, 171615, 18176, 16042, 158, 15845, 60208, 192, 14790, 7409, 785671, 155250, 120413, 79240, 5331, 260, 349291, 11932, 294, 190100, 10613, 836362, 69717, 2991]}, 'Perm': {'d': 20, 'gens': [244357275560799145, 134451162204803282, 19583737563076802]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^3.(S_3\\times D_4)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 36, 'aut_gen_orders': [12, 12, 12, 6, 12, 12, 6, 6], 'aut_gens': [[121666029505671646, 13934578108996513, 262500111643921201], [33143094115241242, 372488434646988083, 499744940165156910], [122734399464342725, 640282005901652856, 257898231186346905], [249713677940482542, 161526640542338253, 160794342856224801], [616471702915877473, 859008770439418816, 122042639647480424], [859049308381174042, 494053766919372083, 499744940165151864], [859049308344841938, 866143441827608284, 390904580940799110], [6423383754053058, 871519378296311736, 629296065402707665], [397662642071163965, 20276798793796536, 262500111680104231]], 'aut_group': '5000.cq', 'aut_hash': 2826640325681291568, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 497664, 'aut_permdeg': 188, 'aut_perms': 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24, 1, 1], [3, 288, 1, 1], [3, 576, 1, 1], [4, 36, 2, 1], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 2], [4, 324, 2, 1], [4, 648, 1, 1], [4, 1296, 1, 2], [6, 2, 1, 1], [6, 6, 1, 1], [6, 8, 1, 1], [6, 8, 2, 3], [6, 8, 4, 1], [6, 12, 1, 6], [6, 12, 2, 1], [6, 24, 1, 6], [6, 24, 2, 6], [6, 24, 4, 3], [6, 48, 1, 2], [6, 48, 2, 2], [6, 72, 2, 3], [6, 72, 4, 1], [6, 144, 1, 3], [6, 144, 2, 5], [6, 144, 4, 2], [6, 216, 1, 2], [6, 288, 1, 1], [6, 288, 2, 1], [6, 432, 1, 3], [6, 576, 1, 1], [6, 576, 2, 1], [6, 648, 2, 1], [6, 1296, 1, 1], [6, 2592, 2, 2], [8, 1296, 1, 2], [9, 576, 1, 1], [9, 576, 2, 1], [12, 72, 2, 3], [12, 72, 4, 1], [12, 144, 1, 3], [12, 144, 2, 5], [12, 144, 4, 2], [12, 216, 1, 2], [12, 432, 1, 7], [12, 432, 2, 1], [12, 648, 2, 1], [12, 864, 1, 1], [12, 1296, 1, 1], [12, 2592, 1, 2], [18, 576, 1, 1], [18, 576, 2, 2], [18, 576, 4, 1], [24, 2592, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_5^4:D_4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 36, 'autcentquo_group': None, 'autcentquo_hash': 219204698074101422, 'autcentquo_nilpotent': False, 'autcentquo_order': 62208, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': '(C_2^2\\times C_3^3:C_2^2).D_6^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 4, 2], [2, 6, 1], [2, 36, 2], [2, 72, 1], [2, 81, 2], [2, 108, 2], [2, 324, 4], [2, 486, 1], [2, 648, 1], [3, 2, 1], [3, 6, 1], [3, 8, 3], [3, 12, 2], [3, 24, 1], [3, 288, 1], [3, 576, 1], [4, 36, 2], [4, 72, 1], [4, 108, 2], [4, 216, 2], [4, 324, 2], [4, 648, 1], [4, 1296, 2], [6, 2, 1], [6, 6, 1], [6, 8, 11], [6, 12, 8], [6, 24, 30], [6, 48, 6], [6, 72, 10], [6, 144, 21], [6, 216, 2], [6, 288, 3], [6, 432, 3], [6, 576, 3], [6, 648, 2], [6, 1296, 1], [6, 2592, 4], [8, 1296, 2], [9, 576, 3], [12, 72, 10], [12, 144, 21], [12, 216, 2], [12, 432, 9], [12, 648, 2], [12, 864, 1], [12, 1296, 1], [12, 2592, 2], [18, 576, 9], [24, 2592, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '31104.ji', 'commutator_count': 1, 'commutator_label': '7776.bj', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '3.1', '3.1'], 'composition_length': 13, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 4, 1, 2], [2, 6, 1, 1], [2, 36, 1, 2], [2, 72, 1, 1], [2, 81, 1, 2], [2, 108, 1, 2], [2, 324, 1, 4], [2, 486, 1, 1], [2, 648, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 8, 1, 3], [3, 12, 1, 2], [3, 24, 1, 1], [3, 288, 1, 1], [3, 576, 1, 1], [4, 36, 1, 2], [4, 72, 1, 1], [4, 108, 1, 2], [4, 216, 1, 2], [4, 324, 1, 2], [4, 648, 1, 1], [4, 1296, 1, 2], [6, 2, 1, 1], [6, 6, 1, 1], [6, 8, 1, 11], [6, 12, 1, 8], [6, 24, 1, 30], [6, 48, 1, 6], [6, 72, 1, 10], [6, 144, 1, 21], [6, 216, 1, 2], [6, 288, 1, 3], [6, 432, 1, 3], [6, 576, 1, 3], [6, 648, 1, 2], [6, 1296, 1, 1], [6, 2592, 1, 4], [8, 1296, 1, 2], [9, 576, 1, 3], [12, 72, 1, 10], [12, 144, 1, 21], [12, 216, 1, 2], [12, 432, 1, 9], [12, 648, 1, 2], [12, 864, 1, 1], [12, 1296, 1, 1], [12, 2592, 1, 2], [18, 576, 1, 9], [24, 2592, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 72, 'exponents_of_order': [8, 5], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[8, 1, 8], [16, 1, 4], [24, 1, 24], [48, 1, 2]], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '7776.bl', 'hash': 3172442348882996740, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 36, 'inner_gen_orders': [6, 12, 12], 'inner_gens': [[121666029505671646, 494053766919330418, 378179607849266310], [397662642071159013, 13934578108996513, 635638286131053339], [33143094078894041, 871519378332776616, 262500111643921201]], 'inner_hash': 1063518838656689817, 'inner_nilpotent': False, 'inner_order': 31104, 'inner_split': None, 'inner_tex': 'C_6^3:(S_3\\times S_4)', 'inner_used': [1, 2, 3], 'irrC_degree': 8, 'irrQ_degree': 8, 'irrQ_dim': 8, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [6, 20], [8, 32], [12, 42], [16, 14], [24, 62], [48, 6]], 'label': '62208.g', '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': 'C6^4:(C2*S4)', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 131, 'number_characteristic_subgroups': 48, 'number_conjugacy_classes': 210, 'number_divisions': 210, 'number_normal_subgroups': 50, 'number_subgroup_autclasses': 13900, 'number_subgroup_classes': 30079, 'number_subgroups': 4039948, 'old_label': None, 'order': 62208, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 2967], [3, 944], [4, 4680], [6, 22224], [8, 2592], [9, 1728], [12, 16704], [18, 5184], [24, 5184]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [160834880801574871, 1110215538558000, 500811828009314551, 43647870], 'outer_gens': [[33143094115241242, 372488434646988083, 499744940165156910], [122734399464342725, 640282005901652856, 257898231186346905], [249713677940482542, 161526640542338253, 160794342856224801], [6423383754053058, 871519378296311736, 629296065402707665]], 'outer_group': '16.14', 'outer_hash': 14, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 16, 'outer_perms': [1328432193090, 2966618070835, 4483583802622, 8597469399120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4', 'pc_rank': 7, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [3, 8], [4, 10], [6, 20], [8, 32], [12, 42], [16, 14], [24, 62], [48, 6]], 'representations': {'PC': {'code': '310762935437346640212582807787892583022909974696645679282695997550644207276071186930972174629706119871785108113881692509488634446863275002997977309459940432580821313032830249384344336135925812065180791041724262221771786331929463898513875677301174221186010236953917055846540565', 'gens': [1, 2, 4, 6, 7, 10, 12], 'pres': [13, 2, 2, 3, 2, 3, 2, 2, 2, 3, 2, 3, 2, 3, 364416, 1251381, 66, 191258, 43683, 49312, 691889, 146, 1784644, 1555337, 744540, 2591, 36522, 101119, 39824, 789522, 2645389, 1088483, 215715, 102160, 7897, 266, 2703175, 1576244, 675825, 49966, 306, 4852232, 2830485, 1213090, 11279, 6336729, 2737822, 1584215, 496128, 7887, 386, 3541834, 1565015, 885492, 329521, 6952, 4942091, 2515992, 2156581, 147002, 61865, 466, 194700, 48697, 2044262, 48762]}, 'Perm': {'d': 20, 'gens': [121666029505671646, 13934578108996513, 262500111643921201]}}, 'schur_multiplier': [2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 64, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^4:(C_2\\times S_4)', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
