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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '13824.fy', 'ambient_counter': 155, 'ambient_order': 13824, 'ambient_tex': 'C_2^6.S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 1, 'characteristic': False, 'core_order': 576, 'counter': 20, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '13824.fy.4.I', 'maximal': True, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': False, 'old_label': '4.i1', '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': 4, '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': '3456.oc', 'subgroup_hash': 1942231094641922994, 'subgroup_order': 3456, 'subgroup_tex': 'D_6^2:S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '13824.fy', 'aut_centralizer_order': None, 'aut_label': '4.I', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '13824.a1', 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': '24.E', 'coset_action_label': None, 'count': 4, 'diagramx': [172, -1, 189, -1], 'generators': [87178291200, 13075, 19342, 174360593048, 93405312000, 39853, 3758, 3036, 7620480, 3991680], 'label': '13824.fy.4.I', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '1.a1', 'normal_contained_in': None, 'normal_contains': None, 'normalizer': '4.I', 'old_label': '4.i1', 'projective_image': '13824.fy', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.I', 'subgroup_fusion': None, 'weyl_group': '3456.oc'}
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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': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 6, 4, 2, 3, 2, 3, 2, 4, 12, 6, 2, 2], 'aut_gens': [[1967901282, 20650453574, 1137300, 13412085385, 1134054, 2587950, 19770831414, 2951738, 647, 526], [131728482, 19771557374, 1137300, 6266978185, 1862886, 1134054, 20649729846, 1500825, 647, 526], [38366295721, 38480887140, 2586614, 6398341006, 1134054, 2587950, 39798138294, 2953385, 265, 647], [38366295060, 20649002535, 2585677, 6398341127, 2587950, 1134054, 39799592190, 3314314, 265, 526], [1967901775, 20650453695, 1137421, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [1968624140, 20649004260, 1860014, 13412085385, 1862886, 1134054, 19771560246, 2950397, 647, 526], [1967901661, 20650453801, 1137535, 13412085385, 1134054, 2587950, 19770831414, 3312825, 647, 526], [1968624489, 20650453338, 1859900, 13412085646, 2587950, 1862886, 19772285310, 2227076, 265, 647], [1969350618, 20649004260, 2586614, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [1967900162, 20649727747, 1861038, 13414673070, 526, 265, 19770469006, 1499368, 1862886, 1134054], [19281634741, 20649003008, 1861164, 33657846407, 1134054, 1862886, 19770831414, 1499237, 265, 526], [38009907198, 20650452637, 1860661, 13412085646, 1862886, 2587950, 19771560246, 2950397, 647, 265], [1967899815, 20649728124, 1136048, 13412085767, 1134054, 1862886, 19770831414, 2953385, 265, 526], [1968624140, 20648639820, 1860014, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526]], 'aut_group': '41472.kr', 'aut_hash': 5131433462079402963, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 41472, 'aut_permdeg': 18, 'aut_perms': [411983379178183, 3749202155315406, 3545741967387042, 963509458501813, 2081150988625839, 3378972814955679, 4843649503987599, 2752595349187335, 381766239340959, 4772987184755438, 304015548606301, 1956044373264270, 3314718500685517], 'aut_phi_ratio': 36.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 2, 1], [2, 3, 3, 1], [2, 6, 1, 1], [2, 9, 1, 1], [2, 9, 6, 1], [2, 12, 1, 1], [2, 18, 2, 1], [2, 27, 3, 1], [2, 36, 2, 1], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 32, 1, 1], [3, 64, 2, 1], [3, 128, 1, 1], [4, 12, 3, 1], [4, 36, 6, 1], [4, 108, 3, 1], [6, 6, 2, 1], [6, 6, 6, 1], [6, 12, 2, 1], [6, 12, 3, 1], [6, 18, 6, 1], [6, 24, 1, 1], [6, 24, 2, 1], [6, 36, 2, 1], [6, 48, 1, 1], [6, 72, 2, 1], [6, 96, 2, 1], [6, 192, 2, 1], [6, 288, 1, 1], [12, 24, 6, 1], [12, 48, 3, 1], [12, 72, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'A_4^2:(C_6^2:D_4)', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 1, 'autcent_group': '1.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 1, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_1', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '41472.kr', 'autcentquo_hash': 5131433462079402963, 'autcentquo_nilpotent': False, 'autcentquo_order': 41472, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'A_4^2:(C_6^2:D_4)', 'cc_stats': [[1, 1, 1], [2, 3, 5], [2, 6, 1], [2, 9, 7], [2, 12, 1], [2, 18, 2], [2, 27, 3], [2, 36, 2], [2, 54, 1], [2, 108, 1], [3, 2, 2], [3, 4, 1], [3, 32, 1], [3, 64, 2], [3, 128, 1], [4, 12, 3], [4, 36, 6], [4, 108, 3], [6, 6, 8], [6, 12, 5], [6, 18, 6], [6, 24, 3], [6, 36, 2], [6, 48, 1], [6, 72, 2], [6, 96, 2], [6, 192, 2], [6, 288, 1], [12, 24, 6], [12, 48, 3], [12, 72, 6]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '3456.oc', 'commutator_count': 1, 'commutator_label': '432.771', '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'], 'composition_length': 10, 'conjugacy_classes_known': True, 'counter': 367, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['6.1', 2], ['96.227', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 5], [2, 6, 1, 1], [2, 9, 1, 7], [2, 12, 1, 1], [2, 18, 1, 2], [2, 27, 1, 3], [2, 36, 1, 2], [2, 54, 1, 1], [2, 108, 1, 1], [3, 2, 1, 2], [3, 4, 1, 1], [3, 32, 1, 1], [3, 64, 1, 2], [3, 128, 1, 1], [4, 12, 1, 3], [4, 36, 1, 6], [4, 108, 1, 3], [6, 6, 1, 8], [6, 12, 1, 5], [6, 18, 1, 6], [6, 24, 1, 3], [6, 36, 1, 2], [6, 48, 1, 1], [6, 72, 1, 2], [6, 96, 1, 2], [6, 192, 1, 2], [6, 288, 1, 1], [12, 24, 1, 6], [12, 48, 1, 3], [12, 72, 1, 6]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 188160, 'exponent': 12, 'exponents_of_order': [7, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[24, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '3456.oc', 'hash': 1942231094641922994, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 3, 3, 2, 2, 2, 6, 4, 2, 2], 'inner_gens': [[1967901282, 38481610203, 1137535, 13412085767, 1862886, 1134054, 39798867126, 1499368, 526, 265], [38008819285, 20650453574, 1740, 13412085767, 1862886, 1134054, 19771560246, 3315793, 526, 265], [1967901661, 20649726974, 1137300, 13412085767, 1862886, 1134054, 19771560246, 2224553, 526, 265], [1967901661, 20650453801, 1137535, 13412085385, 1134054, 2587950, 39798138294, 3312825, 647, 526], [1968624140, 20648639820, 1860014, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1969350618, 20649004260, 2586614, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526], [38365568780, 20648639820, 1860014, 6398340745, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1969350294, 20649003008, 1135922, 13413948006, 647, 526, 19770469127, 2951738, 1134054, 2587950], [1967901540, 20650453338, 1137042, 13412085385, 1134054, 2587950, 19770831414, 2226778, 647, 526], [1967901775, 20650453695, 1137421, 13412085385, 1134054, 2587950, 19770831414, 1501385, 647, 526]], 'inner_hash': 1942231094641922994, 'inner_nilpotent': False, 'inner_order': 3456, 'inner_split': True, 'inner_tex': 'D_6^2:S_4', 'inner_used': [1, 2, 3, 4, 7, 8], 'irrC_degree': 24, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 24, 'irrep_stats': [[1, 8], [2, 12], [3, 24], [4, 6], [6, 28], [8, 1], [12, 10], [24, 1]], 'label': '3456.oc', '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': 'D6^2:S4', 'ngens': 10, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 18, 'number_conjugacy_classes': 90, 'number_divisions': 90, 'number_normal_subgroups': 78, 'number_subgroup_autclasses': 1371, 'number_subgroup_classes': 6076, 'number_subgroups': 108168, 'old_label': None, 'order': 3456, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 447], [3, 296], [4, 576], [6, 1416], [12, 720]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 6], 'outer_gen_pows': [0, 0], 'outer_gens': [[1968624489, 20650453574, 2586735, 13413219174, 265, 526, 19770468745, 3313306, 1862886, 2587950], [491060815, 19770470106, 1137042, 32736131207, 2587950, 1862886, 20650454910, 2226401, 526, 265]], 'outer_group': '12.4', 'outer_hash': 4, 'outer_nilpotent': False, 'outer_order': 12, 'outer_permdeg': 5, 'outer_perms': [6, 31], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6', 'pc_rank': None, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 24], [4, 6], [6, 28], [8, 1], [12, 10], [24, 1]], 'representations': {'PC': {'code': '622303824504332067194411511885159116499883416332385257510299324141683289875953190773847234731181092711588', 'gens': [1, 2, 4, 6, 7, 9, 10], 'pres': [10, 2, 2, 3, 2, 3, 2, 2, 3, 2, 2, 17640, 17481, 51, 39122, 121443, 61693, 30743, 113, 1214, 185765, 28095, 7585, 133566, 40336, 17666, 756, 206, 23057, 697, 42128, 58338, 9748, 129609, 23419, 54929]}, 'Perm': {'d': 14, 'gens': [1967901282, 20650453574, 1137300, 13412085385, 1134054, 2587950, 19770831414, 2951738, 647, 526]}}, 'schur_multiplier': [2, 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': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'D_6^2:S_4', 'transitive_degree': 48, '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': 3, 'aut_exponent': 12, 'aut_gen_orders': [3, 2, 2, 6, 2, 12, 6, 2, 3, 6, 3, 2, 4, 2], 'aut_gens': [[47537280, 87178291200, 127370880, 83838355, 87302037038, 174360593048, 174356582400, 7620480, 93412951822, 40279680, 6314122905, 174396878157], [123379200, 87178291200, 87091200, 43558675, 87261757358, 174360593048, 174356582400, 362880, 93405694222, 127370880, 6267311385, 174483969357], [120113280, 180583603200, 40279680, 79846675, 180623523758, 93412585566, 93405312000, 7620480, 174364222222, 127370880, 6314122905, 93532696088], [47537280, 87178291200, 127370880, 83838355, 87302037038, 93409322648, 93405312000, 7620480, 174364222222, 40279680, 180670705305, 93445607757], [83825280, 180583603200, 127370880, 47550355, 180707349038, 174363844264, 174356582400, 362880, 93405694222, 87091200, 87218581785, 174443711821], [3991680, 87178291200, 127370880, 43558675, 87181923758, 174404138648, 174356582400, 7620480, 93412951822, 40279680, 6314122905, 174396878157], [43545600, 180583603200, 40279680, 47556622, 180623523036, 174440420670, 174356582400, 83462400, 93488787475, 127370880, 87265398849, 174483970598], [120113280, 87178291200, 127370880, 123415473, 87302046355, 174400140990, 174356582400, 39916800, 93445239705, 87091200, 6267302786, 174443689677], [83825280, 87178291200, 127370880, 47556622, 87302044185, 93412580414, 93405312000, 362880, 174356958355, 87091200, 180623886638, 93492439337], [79833600, 180583603200, 87091200, 83827586, 180667076505, 174404119799, 174356582400, 39916800, 93445231836, 127370880, 87218609459, 174483992933], [123379200, 6227020800, 87091200, 43558675, 6310486958, 93409304319, 93405312000, 362880, 174356964622, 127370880, 87218581785, 93532686400], [47537280, 180583603200, 127370880, 83838355, 180707349038, 174360593048, 174356582400, 7620480, 93412951822, 40279680, 87265393305, 174396878157], [83825280, 87178291200, 127370880, 47550355, 87302037038, 174363858968, 174356582400, 362880, 93405694222, 87091200, 6267311385, 174443689677], [43545600, 6227020800, 127370880, 4004755, 6230653358, 93525429544, 93405312000, 39916800, 174396518542, 87091200, 87218581785, 93492405997], [79833600, 87178291200, 127370880, 7270675, 87181923758, 174479980568, 174356582400, 83462400, 93488793742, 40279680, 6314122905, 174396878157]], 'aut_group': '82944.ga', 'aut_hash': 4719265760670157792, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 82944, 'aut_permdeg': 21, 'aut_perms': [2074164194199903, 40036842040506774012, 90011243700812280, 40757438712269661131, 355692262066710, 39540119073460648932, 1957338087197608529, 95935832764064177, 40513310693331171011, 5841406907291729033, 39048455243055692280, 6279640171671753, 5358661914414045231, 4833974461], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 2], [2, 3, 3, 1], [2, 6, 1, 2], [2, 9, 1, 1], [2, 9, 3, 2], [2, 12, 1, 1], [2, 18, 1, 3], [2, 18, 3, 1], [2, 27, 3, 1], [2, 36, 1, 3], [2, 54, 1, 1], [2, 54, 3, 1], [2, 72, 1, 1], [2, 108, 1, 2], [2, 216, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 64, 1, 1], [3, 256, 1, 1], [3, 512, 1, 1], [4, 6, 1, 1], [4, 12, 3, 1], [4, 18, 1, 1], [4, 18, 3, 1], [4, 36, 1, 1], [4, 36, 3, 2], [4, 54, 3, 1], [4, 72, 1, 1], [4, 72, 3, 2], [4, 108, 1, 1], [4, 108, 3, 1], [4, 216, 1, 1], [4, 216, 3, 2], [6, 6, 1, 1], [6, 6, 3, 1], [6, 12, 1, 2], [6, 18, 3, 1], [6, 24, 1, 2], [6, 24, 3, 1], [6, 36, 1, 1], [6, 36, 3, 1], [6, 48, 1, 1], [6, 48, 3, 1], [6, 72, 1, 2], [6, 72, 3, 1], [6, 96, 1, 4], [6, 144, 1, 2], [6, 192, 1, 3], [6, 288, 1, 2], [6, 384, 1, 1], [6, 576, 1, 1], [6, 768, 1, 1], [12, 12, 1, 1], [12, 24, 3, 1], [12, 36, 3, 1], [12, 72, 1, 1], [12, 72, 3, 1], [12, 96, 3, 1], [12, 144, 1, 1], [12, 144, 3, 2], [12, 192, 1, 1], [12, 192, 3, 1], [12, 288, 3, 1], [12, 384, 1, 1], [12, 576, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^6.S_3^4', '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': 12, 'autcentquo_group': '82944.ga', 'autcentquo_hash': 4719265760670157792, 'autcentquo_nilpotent': False, 'autcentquo_order': 82944, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_2^6.S_3^4', 'cc_stats': [[1, 1, 1], [2, 3, 5], [2, 6, 2], [2, 9, 7], [2, 12, 1], [2, 18, 6], [2, 27, 3], [2, 36, 3], [2, 54, 4], [2, 72, 1], [2, 108, 2], [2, 216, 1], [3, 2, 1], [3, 8, 1], [3, 16, 1], [3, 32, 1], [3, 64, 1], [3, 256, 1], [3, 512, 1], [4, 6, 1], [4, 12, 3], [4, 18, 4], [4, 36, 7], [4, 54, 3], [4, 72, 7], [4, 108, 4], [4, 216, 7], [6, 6, 4], [6, 12, 2], [6, 18, 3], [6, 24, 5], [6, 36, 4], [6, 48, 4], [6, 72, 5], [6, 96, 4], [6, 144, 2], [6, 192, 3], [6, 288, 2], [6, 384, 1], [6, 576, 1], [6, 768, 1], [12, 12, 1], [12, 24, 3], [12, 36, 3], [12, 72, 4], [12, 96, 3], [12, 144, 7], [12, 192, 4], [12, 288, 3], [12, 384, 1], [12, 576, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': True, 'central_quotient': '13824.fy', 'commutator_count': 1, 'commutator_label': '1728.47905', 'complements_known': False, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 12, 'conjugacy_classes_known': True, 'counter': 155, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['24.12', 1], ['6.1', 1], ['96.227', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 5], [2, 6, 1, 2], [2, 9, 1, 7], [2, 12, 1, 1], [2, 18, 1, 6], [2, 27, 1, 3], [2, 36, 1, 3], [2, 54, 1, 4], [2, 72, 1, 1], [2, 108, 1, 2], [2, 216, 1, 1], [3, 2, 1, 1], [3, 8, 1, 1], [3, 16, 1, 1], [3, 32, 1, 1], [3, 64, 1, 1], [3, 256, 1, 1], [3, 512, 1, 1], [4, 6, 1, 1], [4, 12, 1, 3], [4, 18, 1, 4], [4, 36, 1, 7], [4, 54, 1, 3], [4, 72, 1, 7], [4, 108, 1, 4], [4, 216, 1, 7], [6, 6, 1, 4], [6, 12, 1, 2], [6, 18, 1, 3], [6, 24, 1, 5], [6, 36, 1, 4], [6, 48, 1, 4], [6, 72, 1, 5], [6, 96, 1, 4], [6, 144, 1, 2], [6, 192, 1, 3], [6, 288, 1, 2], [6, 384, 1, 1], [6, 576, 1, 1], [6, 768, 1, 1], [12, 12, 1, 1], [12, 24, 1, 3], [12, 36, 1, 3], [12, 72, 1, 4], [12, 96, 1, 3], [12, 144, 1, 7], [12, 192, 1, 4], [12, 288, 1, 3], [12, 384, 1, 1], [12, 576, 1, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': None, 'exponent': 12, 'exponents_of_order': [9, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[36, 1, 2]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '13824.fy', 'hash': 5414306939380161149, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [3, 2, 2, 6, 2, 6, 3, 2, 6, 2, 2, 6], 'inner_gens': [[47537280, 87178291200, 40279680, 43558675, 87218211758, 174479980568, 174356582400, 123742080, 93529073422, 87091200, 6354402585, 174443689677], [47537280, 87178291200, 127370880, 83838355, 87302037038, 93409322648, 93405312000, 7620480, 174364222222, 40279680, 180670705305, 93445607757], [123379200, 87178291200, 127370880, 120126355, 87302037038, 174436434968, 174356582400, 83462400, 93488793742, 40279680, 6314122905, 174396878157], [79833600, 87178291200, 87091200, 83838355, 87261757358, 174404120319, 174356582400, 39916800, 93445248142, 127370880, 6267311385, 174483957509], [120113280, 87178291200, 127370880, 123392275, 87302037038, 93448876568, 93405312000, 39916800, 174396518542, 87091200, 180623893785, 93492420831], [79833600, 180583603200, 40279680, 120151859, 180623523758, 174360593048, 174356582400, 3628800, 93408960142, 87091200, 87305698353, 174443712723], [47537280, 180583603200, 127370880, 83838355, 180707349038, 174360593048, 174356582400, 7620480, 93412951822, 40279680, 87265393305, 174396878157], [120113280, 87178291200, 40279680, 79846675, 87218211758, 174363858968, 174356582400, 7620480, 93412951822, 127370880, 6314122905, 174483969357], [120113280, 6227020800, 40279680, 79846675, 6266941358, 174363858968, 174356582400, 7620480, 93412951822, 127370880, 180670705305, 174483965766], [79833600, 87178291200, 127370880, 7270675, 87181923758, 174479980568, 174356582400, 83462400, 93488793742, 40279680, 6314122905, 174396878157], [3991680, 180583603200, 127370880, 43558675, 180587235758, 93452853544, 93405312000, 7620480, 174364222222, 40279680, 6314122905, 93445592301], [79833600, 180583603200, 127370880, 7296179, 180587235036, 174479964709, 174356582400, 83462400, 93488787475, 40279680, 87265418673, 174396878157]], 'inner_hash': 5414306939380161149, 'inner_nilpotent': False, 'inner_order': 13824, 'inner_split': True, 'inner_tex': 'C_2^6.S_3^3', 'inner_used': [1, 2, 3, 4, 5, 6, 8, 11, 12], 'irrC_degree': 36, 'irrQ_degree': 36, 'irrQ_dim': 36, 'irrR_degree': 36, 'irrep_stats': [[1, 8], [2, 12], [3, 32], [4, 6], [6, 36], [8, 1], [9, 24], [12, 12], [18, 16], [24, 1], [36, 2]], 'label': '13824.fy', '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': 'C2^6.S3^3', 'ngens': 12, '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': 90, 'number_characteristic_subgroups': 61, 'number_conjugacy_classes': 150, 'number_divisions': 150, 'number_normal_subgroups': 100, 'number_subgroup_autclasses': 14442, 'number_subgroup_classes': 45568, 'number_subgroups': 1707804, 'old_label': None, 'order': 13824, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 1119], [3, 890], [4, 2976], [6, 4470], [12, 4368]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[47537280, 87178291200, 127370880, 83836185, 87302037038, 174360593048, 174356582400, 7620480, 93412948929, 40279680, 6314125075, 174396878157], [47537280, 87178291200, 127370880, 83836185, 87302052622, 174360593048, 174356582400, 7620480, 93412948929, 40279680, 6314115036, 174396898125]], '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': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 12], [3, 32], [4, 6], [6, 36], [8, 1], [9, 24], [12, 12], [18, 16], [24, 1], [36, 2]], 'representations': {'PC': {'code': '1287161418477357127225264257345744561315316268116842470218625083784079784530998119051588015529194464552290528574241079084946289016060294461563552', 'gens': [1, 2, 4, 6, 8, 9, 10, 11, 12], 'pres': [12, 2, 2, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 241, 61, 290, 1455, 135, 1456, 401777, 67001, 2213, 209, 284274, 47418, 1771, 2647, 396596, 64196, 4916, 11732, 5588, 5829, 4401, 342166, 57070, 9574, 1666, 93335, 15599, 2663, 8291]}, 'Perm': {'d': 15, 'gens': [47537280, 87178291200, 127370880, 83838355, 87302037038, 174360593048, 174356582400, 7620480, 93412951822, 40279680, 6314122905, 174396878157]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 17, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 36, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^6.S_3^3', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': False}
