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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '12960.cy', 'ambient_counter': 77, 'ambient_order': 12960, 'ambient_tex': '(C_3\\times \\GL(2,4)):S_4', 'central': False, 'central_factor': False, 'centralizer_order': 108, 'characteristic': True, 'core_order': 60, 'counter': 205, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '12960.cy.216.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': True, 'nilpotent': False, 'normal': True, 'old_label': '216.a1', 'outer_equivalence': True, 'perfect': True, 'proper': True, 'quotient': '216.165', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 165, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 216, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_3^2:S_4', 'simple': True, 'solvable': False, 'special_labels': ['PC', 'D3', 'PC', 'D3'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '60.5', 'subgroup_hash': 5, 'subgroup_order': 60, 'subgroup_tex': 'A_5', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '12960.cy', 'aut_centralizer_order': None, 'aut_label': '216.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '120.a1', 'complements': ['60.m1', '60.l1', '60.o1', '60.u1'], 'conjugacy_class_count': 1, 'contained_in': ['72.a1', '72.h1', '108.c1', '108.f1'], 'contains': ['1080.z1', '1296.b1', '2160.f1'], 'core': '216.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3799, 5591, 668, 5538], 'generators': [10824, 609], 'label': '12960.cy.216.a1', 'mobius_quo': -1, 'mobius_sub': -2916, 'normal_closure': '216.a1', 'normal_contained_in': ['54.a1', '72.a1'], 'normal_contains': ['12960.a1'], 'normalizer': '1.a1', 'old_label': '216.a1', 'projective_image': '12960.cy', 'quotient_action_image': '2.1', 'quotient_action_kernel': '108.41', 'quotient_action_kernel_order': 108, 'quotient_fusion': None, 'short_label': '216.a1', 'subgroup_fusion': None, 'weyl_group': '120.34'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '1.1', 'all_subgroups_known': True, 'almost_simple': True, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 1, 'aut_exponent': 60, 'aut_gen_orders': [2, 5], 'aut_gens': [[33, 30], [42, 45], [52, 20]], 'aut_group': '120.34', 'aut_hash': 34, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 120, 'aut_permdeg': 5, 'aut_perms': [24, 33], 'aut_phi_ratio': 7.5, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [3, 20, 1, 1], [5, 12, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_5', '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': 60, 'autcentquo_group': '120.34', 'autcentquo_hash': 34, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_5', 'cc_stats': [[1, 1, 1], [2, 15, 1], [3, 20, 1], [5, 12, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '60.5', 'commutator_count': 1, 'commutator_label': '60.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['60.5'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 5, 'cyclic': False, 'derived_length': 0, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 15, 1, 1], [3, 20, 1, 1], [5, 12, 2, 1]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 19, 'exponent': 30, 'exponents_of_order': [2, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [[3, 1, 2], [4, 1, 1], [5, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '60.5', 'hash': 5, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [5, 3], 'inner_gens': [[33, 8], [85, 30]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'A_5', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 4, 'irrQ_dim': 4, 'irrR_degree': 3, 'irrep_stats': [[1, 1], [3, 2], [4, 1], [5, 1]], 'label': '60.5', 'linC_count': 2, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': False, 'name': 'A5', 'ngens': 2, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 4, 'number_characteristic_subgroups': 2, 'number_conjugacy_classes': 5, 'number_divisions': 4, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 9, 'number_subgroups': 59, 'old_label': None, 'order': 60, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 15], [3, 20], [5, 24]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [20], 'outer_gens': [[112, 56]], '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': True, 'permutation_degree': 5, 'pgroup': 0, 'primary_abelian_invariants': [], 'quasisimple': True, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [4, 1], [5, 1], [6, 1]], 'representations': {'GLZ': {'b': 3, 'd': 4, 'gens': [40673960, 19414147]}, 'Lie': [{'d': 2, 'q': 4, 'gens': [194, 21], 'family': 'SL'}, {'d': 2, 'q': 4, 'gens': [194, 21], 'family': 'PSL'}, {'d': 2, 'q': 5, 'gens': [109, 377], 'family': 'PSL'}, {'d': 2, 'q': 4, 'gens': [66, 21], 'family': 'PGL'}, {'d': 3, 'q': 4, 'gens': [4373, 131331, 4368], 'family': 'SO'}, {'d': 2, 'q': 4, 'gens': [28678, 273], 'family': 'SU'}, {'d': 3, 'q': 4, 'gens': [4373, 131331, 4368], 'family': 'PSO'}, {'d': 2, 'q': 4, 'gens': [28678, 273], 'family': 'PSU'}, {'d': 2, 'q': 5, 'gens': [10579, 46877], 'family': 'PSU'}, {'d': 3, 'q': 4, 'gens': [4373, 131331, 4368], 'family': 'GO'}, {'d': 3, 'q': 4, 'gens': [196866, 4373], 'family': 'Omega'}, {'d': 3, 'q': 5, 'gens': [65611, 1563129], 'family': 'Omega'}, {'d': 4, 'q': 2, 'gens': [33377, 5931], 'family': 'OmegaMinus'}, {'d': 3, 'q': 4, 'gens': [4373, 131331, 4368], 'family': 'PGO'}, {'d': 2, 'q': 4, 'gens': [57346, 273], 'family': 'PGU'}, {'d': 3, 'q': 4, 'gens': [196866, 4373], 'family': 'POmega'}, {'d': 3, 'q': 5, 'gens': [65611, 1563129], 'family': 'POmega'}, {'d': 4, 'q': 2, 'gens': [33377, 5931], 'family': 'POmegaMinus'}, {'d': 4, 'q': 2, 'gens': [194, 21], 'family': 'SpinMinus'}, {'d': 2, 'q': 4, 'gens': [28678, 273], 'family': 'CSU'}, {'d': 2, 'q': 5, 'gens': [109, 377], 'family': 'PSigmaL'}], 'GLFp': {'d': 3, 'p': 5, 'gens': [1269282, 1294106]}, 'Perm': {'d': 5, 'gens': [33, 30]}}, 'schur_multiplier': [2], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'A_5', 'transitive_degree': 5, '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': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 360, 'aut_gen_orders': [8, 12, 6, 24], 'aut_gens': [[127370880, 6266937707, 180591242059, 174360577830, 47537280, 174356582400, 40279680], [127370880, 6227423585, 87185931076, 47541030, 3994712, 174356585432, 40279680], [127370880, 180591227456, 87218247367, 93448861350, 120113280, 3750, 87091200], [40279680, 87185912315, 6230662627, 174436419750, 3994712, 174356582400, 87091200], [87091200, 180587235150, 180583987061, 174479965350, 174360574080, 93405315750, 127370880]], 'aut_group': None, 'aut_hash': 2363374880214477228, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 11197440, 'aut_permdeg': 540, 'aut_perms': 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'aut_phi_ratio': 3240.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 1, 1], [2, 45, 1, 1], [2, 540, 1, 1], [3, 2, 4, 1], [3, 8, 9, 1], [3, 20, 1, 1], [3, 40, 4, 1], [3, 160, 9, 1], [4, 540, 1, 1], [4, 1620, 1, 2], [5, 24, 1, 1], [6, 6, 4, 1], [6, 30, 4, 1], [6, 60, 1, 1], [6, 90, 4, 1], [6, 120, 4, 1], [6, 120, 9, 1], [6, 1080, 1, 1], [10, 72, 1, 1], [12, 1080, 1, 1], [15, 24, 8, 1], [15, 96, 18, 1], [30, 72, 8, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4.Q_8.(S_3\\times S_4).S_5', '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': 360, 'autcentquo_group': None, 'autcentquo_hash': 2363374880214477228, 'autcentquo_nilpotent': False, 'autcentquo_order': 11197440, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4.Q_8.(S_3\\times S_4).S_5', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 15, 1], [2, 45, 1], [2, 540, 1], [3, 2, 4], [3, 8, 9], [3, 20, 1], [3, 40, 4], [3, 160, 9], [4, 540, 1], [4, 1620, 2], [5, 24, 1], [6, 6, 4], [6, 30, 4], [6, 60, 1], [6, 90, 4], [6, 120, 13], [6, 1080, 1], [10, 72, 1], [12, 1080, 1], [15, 24, 8], [15, 96, 18], [30, 72, 8]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '12960.cy', 'commutator_count': 1, 'commutator_label': '6480.dn', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1', '60.5'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 77, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 15, 1, 1], [2, 45, 1, 1], [2, 540, 1, 1], [3, 2, 1, 4], [3, 8, 1, 9], [3, 20, 1, 1], [3, 40, 1, 4], [3, 160, 1, 9], [4, 540, 1, 1], [4, 1620, 1, 2], [5, 24, 1, 1], [6, 6, 1, 4], [6, 30, 1, 4], [6, 60, 1, 1], [6, 90, 1, 4], [6, 120, 1, 13], [6, 1080, 1, 1], [10, 72, 1, 1], [12, 1080, 1, 1], [15, 24, 2, 4], [15, 96, 2, 9], [30, 72, 2, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 1308954465, 'exponent': 60, 'exponents_of_order': [5, 4, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '12960.cy', 'hash': 2658931717656400530, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 2, 6, 3, 3, 3, 2], 'inner_gens': [[127370880, 6227383787, 180667083979, 174436419750, 123379200, 174356582400, 40279680], [87091200, 6266937707, 87302073425, 93489140312, 120113280, 93405312000, 40279680], [40279680, 87302046992, 180591242059, 93412572632, 120113280, 93405312000, 127370880], [40279680, 87261756709, 6230668702, 174360577830, 79833600, 174356582400, 87091200], [40279680, 6234641387, 180707363659, 174479965350, 47537280, 174356582400, 87091200], [127370880, 87218208107, 6234659659, 174360577830, 47537280, 174356582400, 40279680], [127370880, 6266937707, 180667083979, 174479965350, 79833600, 174356582400, 40279680]], 'inner_hash': 2658931717656400530, 'inner_nilpotent': False, 'inner_order': 12960, 'inner_split': True, 'inner_tex': '(C_3\\times \\GL(2,4)):S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [2, 13], [3, 2], [4, 2], [5, 2], [6, 31], [8, 13], [10, 13], [12, 2], [15, 2], [18, 9], [24, 4], [30, 4]], 'label': '12960.cy', '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': False, 'name': '(C3*GL(2,4)):S4', 'ngens': 7, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 26, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 99, 'number_divisions': 82, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 449, 'number_subgroup_classes': 2466, 'number_subgroups': 273828, 'old_label': None, 'order': 12960, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 603], [3, 1700], [4, 3780], [5, 24], [6, 3204], [10, 72], [12, 1080], [15, 1920], [30, 576]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 4, 2, 4, 3, 2, 6, 6], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[87091200, 6266937707, 87302052382, 93489140312, 120113280, 93405312000, 40279680], [87091200, 6266937707, 87302051659, 83825280, 174476695680, 174356586150, 40279680], [127370880, 6266937707, 87185930059, 93409307430, 47540312, 93405312000, 40279680], [87091200, 6266937707, 87302049383, 174440410712, 93525429030, 3750, 40279680], [127370880, 6266937707, 87185927783, 3991680, 93452852312, 174356582400, 40279680], [127370880, 6266937707, 87185930059, 93409307430, 47537280, 93405312000, 40279680], [87091200, 6266937707, 6350778983, 174440407680, 93525429030, 93405312000, 40279680], [87091200, 6266937707, 6350778983, 93489141030, 174476699430, 174356585432, 40279680]], 'outer_group': '864.4661', 'outer_hash': 4661, 'outer_nilpotent': False, 'outer_order': 864, 'outer_permdeg': 11, 'outer_perms': [1, 8252041, 16511160, 19073167, 13246206, 2038560, 18292321, 11139391], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times C_3^2:\\GL(2,3)', 'pc_rank': None, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 13], [3, 2], [4, 2], [5, 2], [6, 5], [8, 13], [10, 13], [12, 15], [15, 2], [18, 1], [24, 4], [30, 4], [36, 4]], 'representations': {'Perm': {'d': 15, 'gens': [127370880, 6266937707, 180591242059, 174360577830, 47537280, 174356582400, 40279680]}}, 'schur_multiplier': [3, 6, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 13, 'solvable': False, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times \\GL(2,4)):S_4', 'transitive_degree': 180, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 72, 'aut_gen_orders': [2, 2, 2, 2, 3, 2, 2, 3, 3], 'aut_gens': [[40345, 45507, 144, 148, 367920, 806400], [40345, 80884, 144, 148, 806400, 367920], [40345, 45360, 4, 148, 367920, 806400], [40345, 45363, 240, 4, 367920, 806400], [40345, 725907, 144, 148, 367920, 806400], [40586, 45507, 144, 148, 367920, 806400], [40345, 45600, 144, 243, 367920, 806400], [1134025, 1129107, 144, 148, 367920, 806400], [40441, 45507, 144, 148, 367920, 806400], [85802, 45507, 144, 148, 1174320, 367920]], 'aut_group': '93312.jr', 'aut_hash': 7211166090879777373, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 93312, 'aut_permdeg': 31, 'aut_perms': [65758909511913611102344579805, 97710843914081409953165516818560, 29683090601387201498813671237320, 16, 1980733759795531023896470538581920, 1579853970287315571264708862080, 7, 292725590573433126986456181557880, 841865860084755513106525351172523], 'aut_phi_ratio': 1296.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 2, 4, 1], [3, 8, 9, 1], [4, 54, 1, 1], [6, 6, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_3^4:(S_4\\times \\GL(2,3))', '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': 72, 'autcentquo_group': '93312.jr', 'autcentquo_hash': 7211166090879777373, 'autcentquo_nilpotent': False, 'autcentquo_order': 93312, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^4:(S_4\\times \\GL(2,3))', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 54, 1], [3, 2, 4], [3, 8, 9], [4, 54, 1], [6, 6, 4]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '216.165', 'commutator_count': 1, 'commutator_label': '108.41', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 165, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 54, 1, 1], [3, 2, 1, 4], [3, 8, 1, 9], [4, 54, 1, 1], [6, 6, 1, 4]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 12285, 'exponent': 12, 'exponents_of_order': [3, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '216.165', 'hash': 165, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 3, 3, 2, 2], 'inner_gens': [[40345, 80884, 240, 243, 806400, 367920], [5309, 45507, 144, 148, 806400, 1174320], [40585, 45507, 144, 148, 367920, 806400], [40586, 45507, 144, 148, 367920, 806400], [1134025, 1129107, 144, 148, 367920, 806400], [1134025, 448707, 144, 148, 367920, 806400]], 'inner_hash': 165, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2:S_4', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 2], [2, 13], [3, 2], [6, 4]], 'label': '216.165', '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': 'C3^2:S4', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 7, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 21, 'number_divisions': 21, 'number_normal_subgroups': 35, 'number_subgroup_autclasses': 33, 'number_subgroup_classes': 130, 'number_subgroups': 1060, 'old_label': None, 'order': 216, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 57], [3, 80], [4, 54], [6, 24]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 24, 'outer_gen_orders': [2, 3, 3], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[40345, 45507, 240, 4, 367920, 806400], [40345, 45507, 3, 148, 367920, 806400], [40345, 45603, 144, 148, 367920, 806400]], 'outer_group': '432.734', 'outer_hash': 734, 'outer_nilpotent': False, 'outer_order': 432, 'outer_permdeg': 9, 'outer_perms': [10829, 35711, 52564], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_3^2:\\GL(2,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 13], [3, 2], [6, 4]], 'representations': {'PC': {'code': 8909543178979295278179679509, 'gens': [1, 2, 3, 5], 'pres': [6, 2, 3, 2, 3, 2, 3, 49, 542, 1034, 50, 579, 5944, 2440, 88, 5189]}, 'GLZN': {'d': 2, 'p': 36, 'gens': [47089, 909811, 1081075, 502525, 1197949, 70633]}, 'Perm': {'d': 10, 'gens': [40345, 45507, 144, 148, 367920, 806400]}}, 'schur_multiplier': [3, 3, 6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:S_4', 'transitive_degree': 36, 'wreath_data': None, 'wreath_product': False}
