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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '864.2237', 'ambient_counter': 2237, 'ambient_order': 864, 'ambient_tex': 'C_3^2:(C_4\\times S_4)', 'central': True, 'central_factor': False, 'centralizer_order': 864, 'characteristic': True, 'core_order': 2, 'counter': 222, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '864.2237.432.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '432.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '432.523', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 523, 'quotient_metabelian': False, 'quotient_nilpotent': False, 'quotient_order': 432, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': False, 'quotient_tex': 'C_6^2:D_6', 'simple': True, 'solvable': True, 'special_labels': ['Z', 'U0'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2.1', 'subgroup_hash': 1, 'subgroup_order': 2, 'subgroup_tex': 'C_2', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '864.2237', 'aut_centralizer_order': 1728, 'aut_label': '432.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 1728, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['144.a1.a1', '144.b1.a1', '144.c1.a1', '144.d1.a1', '216.b1.a1', '216.c1.a1', '216.d1.a1', '216.e1.a1', '216.f1.a1'], 'contains': ['864.a1.a1'], 'core': '432.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5549, 5385, 3605, 7533, 4832, 5121, 5907, 5042], 'generators': [12], 'label': '864.2237.432.a1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '432.a1.a1', 'normal_contained_in': ['108.a1.a1', '144.a1.a1'], 'normal_contains': ['864.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '432.a1.a1', 'projective_image': '432.523', 'quotient_action_image': '1.1', 'quotient_action_kernel': '432.523', 'quotient_action_kernel_order': 432, 'quotient_fusion': None, 'short_label': '432.a1.a1', 'subgroup_fusion': None, 'weyl_group': '1.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 0, 'aut_exponent': 1, 'aut_gen_orders': [], 'aut_gens': [[1]], 'aut_group': '1.1', 'aut_hash': 1, 'aut_nilpotency_class': 0, 'aut_nilpotent': True, 'aut_order': 1, 'aut_permdeg': 1, 'aut_perms': [], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_1', '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': 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, 1]], 'center_label': '2.1', 'center_order': 2, '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': ['2.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [1], 'factors_of_aut_order': [], 'factors_of_order': [2], 'faithful_reps': [[1, 1, 1]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '2.1', 'hash': 1, 'hyperelementary': 2, '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': 1, 'irrQ_dim': 1, 'irrR_degree': 1, 'irrep_stats': [[1, 2]], 'label': '2.1', 'linC_count': 1, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 1, 'linQ_degree_count': 1, 'linQ_dim': 1, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 1, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2', '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': 2, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 2, 'order_factorization_type': 1, 'order_stats': [[1, 1], [2, 1]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 2, 'pgroup': 2, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 1, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [12]}, 'Lie': [{'d': 2, 'q': 2, 'gens': [6], 'family': 'CSOPlus'}, {'d': 2, 'q': 2, 'gens': [6], 'family': 'COPlus'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'AGammaL'}, {'d': 1, 'q': 2, 'gens': [1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [11]}, 'Perm': {'d': 2, 'gens': [1]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [2], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2', 'transitive_degree': 2, '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': '8.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 2, 24, 144], [1, 14, 120, 720], [1, 10, 552, 144], [1, 14, 24, 144], [13, 2, 24, 144], [17, 2, 456, 696], [1, 338, 24, 144], [97, 98, 24, 144], [433, 74, 24, 144], [1, 506, 24, 144]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 54, 'aut_perms': [226665416010892249111424233135328923941084176305250702396737737252178359, 170111256216717899370406480175665436973468247523096548448111777125862046, 14271549506680906379712800286327181627787633802734803427524608000000, 218828793683201130582489793379649529557130296216793048349438458632373002, 174789768034058263676275101246291580692536961415233910882653687643957298, 226976850809001467601649669189228846701806210663122266174883992645045392, 227312172219184964655817822505881100858579933432315463451641245384373392, 1695404118180710464195103835026677410135411256994906091826197738931200, 211246925366099423921849318883013105811337725893283556603823506600591480], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 2, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 2, 1], [4, 18, 2, 3], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 5], [6, 12, 1, 2], [6, 24, 1, 1], [6, 36, 2, 1], [6, 48, 1, 1], [12, 36, 2, 3], [12, 72, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', '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': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 18, 2], [3, 2, 1], [3, 6, 1], [3, 24, 1], [3, 48, 1], [4, 9, 2], [4, 18, 6], [4, 27, 2], [6, 2, 1], [6, 6, 5], [6, 12, 2], [6, 24, 1], [6, 36, 2], [6, 48, 1], [12, 36, 6], [12, 72, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '432.523', 'commutator_count': 1, 'commutator_label': '108.22', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 2237, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 18, 1, 2], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 9, 2, 1], [4, 18, 1, 2], [4, 18, 2, 2], [4, 27, 2, 1], [6, 2, 1, 1], [6, 6, 1, 5], [6, 12, 1, 2], [6, 24, 1, 1], [6, 36, 1, 2], [6, 48, 1, 1], [12, 36, 1, 2], [12, 36, 2, 2], [12, 72, 2, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 54, 'exponent': 12, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2], [12, -1, 1]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '144.183', 'hash': 2237, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 10, 552, 144], [17, 2, 552, 312], [481, 482, 24, 144], [1, 842, 24, 144]], 'inner_hash': 523, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 8], [3, 8], [4, 2], [6, 12], [12, 2]], 'label': '864.2237', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 8, 'linQ_dim': 8, 'linQ_dim_count': 4, 'linR_count': 4, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:(C4*S4)', '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': 29, 'number_characteristic_subgroups': 23, 'number_conjugacy_classes': 40, 'number_divisions': 33, 'number_normal_subgroups': 27, 'number_subgroup_autclasses': 201, 'number_subgroup_classes': 227, 'number_subgroups': 1914, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 43], [3, 80], [4, 180], [6, 200], [12, 360]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2], 'outer_gen_pows': [0, 0], 'outer_gens': [[1, 22, 456, 720], [13, 10, 456, 720]], 'outer_group': '4.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [1, 6], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 4], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 8], [3, 4], [4, 3], [6, 10], [12, 4]], 'representations': {'PC': {'code': 7623255552497281462628366739182018130041449627364724391213012080149, 'gens': [1, 2, 5, 7], 'pres': [8, 2, 2, 2, 3, 2, 3, 2, 3, 161, 41, 482, 66, 515, 22084, 11052, 5300, 2308, 116, 4613, 2317, 8750, 2374, 4902, 166, 19983, 5399, 3103]}, 'Perm': {'d': 17, 'gens': [355938468489, 2965618656720, 16, 23801712884040, 4036071473280, 47450457694080, 5160, 11520]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:(C_4\\times S_4)', '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 6, 6, 6], 'aut_gens': [[1, 2, 12, 72], [1, 10, 276, 72], [9, 2, 276, 156], [265, 266, 12, 72], [1, 158, 12, 72]], 'aut_group': '432.523', 'aut_hash': 523, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 432, 'aut_permdeg': 27, 'aut_perms': [4928320639101413757507308547, 1704461186941630566738363965, 63152356070716317549984080, 3726611319080708356243034274], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 18, 1, 2], [2, 27, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 18, 1, 2], [6, 6, 1, 2], [6, 12, 1, 1], [6, 36, 1, 2], [6, 72, 1, 1], [12, 36, 1, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2:D_6', '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': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 9, 1], [2, 18, 2], [2, 27, 1], [3, 2, 1], [3, 6, 1], [3, 24, 1], [3, 48, 1], [4, 18, 2], [6, 6, 2], [6, 12, 1], [6, 36, 2], [6, 72, 1], [12, 36, 2]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '432.523', 'commutator_count': 1, 'commutator_label': '108.22', 'complements_known': True, 'complete': True, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 523, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 9, 1, 1], [2, 18, 1, 2], [2, 27, 1, 1], [3, 2, 1, 1], [3, 6, 1, 1], [3, 24, 1, 1], [3, 48, 1, 1], [4, 18, 1, 2], [6, 6, 1, 2], [6, 12, 1, 1], [6, 36, 1, 2], [6, 72, 1, 1], [12, 36, 1, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 54, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 1, 2], [12, 1, 1]], 'familial': False, 'frattini_label': '3.1', 'frattini_quotient': '144.183', 'hash': 523, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 6, 6, 6], 'inner_gens': [[1, 10, 276, 72], [5, 2, 240, 420], [241, 278, 12, 72], [1, 158, 12, 72]], 'inner_hash': 523, 'inner_nilpotent': False, 'inner_order': 432, 'inner_split': True, 'inner_tex': 'C_6^2:D_6', 'inner_used': [1, 2, 3, 4], 'irrC_degree': 6, 'irrQ_degree': 6, 'irrQ_dim': 6, 'irrR_degree': 6, 'irrep_stats': [[1, 4], [2, 4], [3, 4], [4, 1], [6, 6], [12, 1]], 'label': '432.523', 'linC_count': 2, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 2, 'linQ_dim': 6, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C6^2:D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 20, 'number_characteristic_subgroups': 15, 'number_conjugacy_classes': 20, 'number_divisions': 20, 'number_normal_subgroups': 15, 'number_subgroup_autclasses': 134, 'number_subgroup_classes': 134, 'number_subgroups': 1289, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 75], [3, 80], [4, 36], [6, 168], [12, 72]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 1, 'outer_gen_orders': [], 'outer_gen_pows': [], 'outer_gens': [], 'outer_group': '1.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 1, 'outer_permdeg': 1, 'outer_perms': [], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_1', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 4], [3, 4], [4, 1], [6, 6], [12, 1]], 'representations': {'PC': {'code': 3787299631419662838001599751597083946264950037, 'gens': [1, 2, 4, 6], 'pres': [7, 2, 2, 3, 2, 3, 2, 3, 141, 36, 170, 7731, 3370, 1613, 80, 1684, 851, 8832, 3673, 124, 8245, 2372]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [73186577632889731, 75460041430583719]}, 'Perm': {'d': 13, 'gens': [14963880, 94484882, 569898723, 124912200, 1133687640, 7, 16]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_6^2:D_6', 'transitive_degree': 18, 'wreath_data': None, 'wreath_product': False}
