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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '1584.135', 'ambient_counter': 135, 'ambient_order': 1584, 'ambient_tex': 'D_{44}:C_{18}', 'central': True, 'central_factor': False, 'centralizer_order': 1584, 'characteristic': True, 'core_order': 6, 'counter': 104, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '1584.135.264.a1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '264.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '264.36', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 36, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 264, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_6\\times D_{22}', 'simple': False, 'solvable': True, 'special_labels': ['Phi'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '6.2', 'subgroup_hash': 2, 'subgroup_order': 6, 'subgroup_tex': 'C_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1584.135', 'aut_centralizer_order': 5280, 'aut_label': '264.a1', 'aut_quo_index': 12, 'aut_stab_index': 1, 'aut_weyl_group': '2.1', 'aut_weyl_index': 5280, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1', '132.d1.a1', '132.d1.b1', '132.e1.a1', '132.e1.b1'], 'contains': ['528.a1.a1', '792.a1.a1'], 'core': '264.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4281, 7046, 4557, 7380, 5084, 4975, 5345, 5826], 'generators': [24778026504, 2127406316], 'label': '1584.135.264.a1.a1', 'mobius_quo': 1, 'mobius_sub': -88, 'normal_closure': '264.a1.a1', 'normal_contained_in': ['24.a1.a1', '88.a1.a1', '132.a1.a1', '132.b1.a1', '132.c1.a1'], 'normal_contains': ['528.a1.a1', '792.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '264.a1.a1', 'projective_image': '264.36', 'quotient_action_image': '1.1', 'quotient_action_kernel': '264.36', 'quotient_action_kernel_order': 264, 'quotient_fusion': None, 'short_label': '264.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': '6.2', '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], [5]], '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], [2, 1, 1, 1], [3, 1, 2, 1], [6, 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], [2, 1, 1], [3, 1, 2], [6, 1, 2]], 'center_label': '6.2', 'center_order': 6, 'central_product': True, 'central_quotient': '1.1', 'commutator_count': 0, 'commutator_label': '1.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '3.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 1, 2, 1], [6, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 6, 'eulerian_function': 1, 'exponent': 6, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '6.2', 'hash': 2, 'hyperelementary': 6, '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, 6]], 'label': '6.2', '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': 'C6', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 6, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 6, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [3, 2], [6, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[5]], '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': 5, 'pgroup': 0, 'primary_abelian_invariants': [2, 3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 2]], 'representations': {'PC': {'code': 21, 'gens': [1], 'pres': [2, -2, -3, 4]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [73]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [31, 56]}, 'Perm': {'d': 5, 'gens': [24, 4]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [6], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6', 'transitive_degree': 6, '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': '72.18', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 660, 'aut_gen_orders': [30, 30, 30, 10, 30, 30], 'aut_gens': [[20085218158, 15767835078, 158006], [8071630041, 13390145691, 39829422], [19084085794, 125141745, 2630125], [11137597909, 24715455533, 52496104], [22212624680, 22838332207, 42481779], [10824743978, 16831538151, 19925033], [1439128060, 500566333, 19694773]], 'aut_group': None, 'aut_hash': 569556090490505273, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 10560, 'aut_permdeg': 52, 'aut_perms': [48321365600027051791705374226123915231552038434527987942974801234328, 53529491512083415265386096238883155640531079342338147044980537600, 41602690302509284389960037993933877387991798471346123225459346867786, 43594822256310757593559926513812906605673710575960074655020038322758, 26186394043978570311966781269705826796530566250827259238131247334637, 12752130449931557312787887936856259303113686997176769413755472523513], 'aut_phi_ratio': 22.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 2, 1], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 22, 2, 1], [6, 1, 2, 1], [6, 2, 2, 1], [6, 22, 4, 1], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 22, 4, 1], [18, 1, 6, 1], [18, 2, 6, 1], [18, 22, 12, 1], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 22, 12, 1], [44, 2, 10, 2], [66, 2, 10, 1], [66, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{22}.C_{30}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '48.52', 'autcent_hash': 52, 'autcent_nilpotent': True, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times C_6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '220.7', 'autcentquo_hash': 7, 'autcentquo_nilpotent': False, 'autcentquo_order': 220, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 22, 2], [3, 1, 2], [4, 1, 2], [4, 2, 1], [4, 22, 2], [6, 1, 2], [6, 2, 2], [6, 22, 4], [9, 1, 6], [11, 2, 5], [12, 1, 4], [12, 2, 2], [12, 22, 4], [18, 1, 6], [18, 2, 6], [18, 22, 12], [22, 2, 15], [33, 2, 10], [36, 1, 12], [36, 2, 6], [36, 22, 12], [44, 2, 20], [66, 2, 30], [99, 2, 30], [132, 2, 40], [198, 2, 90], [396, 2, 120]], 'center_label': '36.2', 'center_order': 36, 'central_product': True, 'central_quotient': '44.3', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 135, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['176.30', 1], ['9.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 22, 1, 2], [3, 1, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 22, 1, 2], [6, 1, 2, 1], [6, 2, 2, 1], [6, 22, 2, 2], [9, 1, 6, 1], [11, 2, 5, 1], [12, 1, 4, 1], [12, 2, 2, 1], [12, 22, 2, 2], [18, 1, 6, 1], [18, 2, 6, 1], [18, 22, 6, 2], [22, 2, 5, 1], [22, 2, 10, 1], [33, 2, 10, 1], [36, 1, 12, 1], [36, 2, 6, 1], [36, 22, 6, 2], [44, 2, 10, 2], [66, 2, 10, 1], [66, 2, 20, 1], [99, 2, 30, 1], [132, 2, 20, 2], [198, 2, 30, 1], [198, 2, 60, 1], [396, 2, 60, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 117936, 'exponent': 396, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [[2, 0, 120]], 'familial': False, 'frattini_label': '6.2', 'frattini_quotient': '264.36', 'hash': 135, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [22, 22, 2], 'inner_gens': [[20085218158, 15767835078, 60098257], [20085218158, 15767835078, 19694773], [1564269646, 17644958238, 158006]], 'inner_hash': 3, 'inner_nilpotent': False, 'inner_order': 44, 'inner_split': True, 'inner_tex': 'D_{22}', 'inner_used': [1, 3], 'irrC_degree': 2, 'irrQ_degree': 240, 'irrQ_dim': 240, 'irrR_degree': 4, 'irrep_stats': [[1, 72], [2, 378]], 'label': '1584.135', 'linC_count': 120, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 32, 'linQ_dim': 20, 'linQ_dim_count': 32, 'linR_count': 60, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'D44:C18', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 36, 'number_characteristic_subgroups': 45, 'number_conjugacy_classes': 450, 'number_divisions': 42, 'number_normal_subgroups': 69, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 120, 'number_subgroups': 588, 'old_label': None, 'order': 1584, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 47], [3, 2], [4, 48], [6, 94], [9, 6], [11, 10], [12, 96], [18, 282], [22, 30], [33, 20], [36, 288], [44, 40], [66, 60], [99, 60], [132, 80], [198, 180], [396, 240]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 30, 'outer_gen_orders': [2, 2, 2, 30], 'outer_gen_pows': [62570774, 62570774, 62570774, 19522081261], 'outer_gens': [[23276327632, 7195639040, 158006], [23276327632, 17644958238, 158006], [7946488521, 15767835078, 158006], [23401469218, 24340030945, 52666417]], 'outer_group': '240.208', 'outer_hash': 208, 'outer_nilpotent': True, 'outer_order': 240, 'outer_permdeg': 16, 'outer_perms': [40279680, 1307674368000, 362880, 6227026593], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3\\times C_{30}', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 28, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 9], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [4, 1], [6, 8], [8, 1], [10, 4], [20, 4], [24, 1], [40, 1], [60, 4], [80, 1], [240, 1]], 'representations': {'PC': {'code': 302294354905805879501193278953540000119, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, 2, -3, -3, -11, 36, 24531, 80, 5604, 137, 20165, 166, 70566]}, 'GLFp': {'d': 2, 'p': 397, 'gens': [20085218158, 15767835078, 158006]}, 'Perm': {'d': 28, 'gens': [10921132818399422783324528047, 23020551001543316243742720000, 1629375110092645594398720000, 135184941877708800, 34341896591985019623505920000, 263631088065945600, 4364893]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 18], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_{44}:C_{18}', 'transitive_degree': 792, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [10, 2, 6, 2, 22], 'aut_gens': [[1, 2, 4], [1, 2, 140], [1, 2, 5], [132, 134, 173], [1, 3, 4], [1, 63, 4]], 'aut_group': '5280.ba', 'aut_hash': 96918778551754254, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 5280, 'aut_permdeg': 46, 'aut_perms': [5380898799971124519305286530898667320459356643736523938848, 60416078979029077125010216234857032888512914466927926, 5056014435510809753696331010662447150083132575050265352236, 119682636944982246551787837421004879270856180839790761647, 3788777576975469777801478315086642323765175957538038185935], 'aut_phi_ratio': 66.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 11, 4, 1], [3, 1, 2, 1], [6, 1, 6, 1], [6, 11, 8, 1], [11, 2, 5, 1], [22, 2, 15, 1], [33, 2, 10, 1], [66, 2, 30, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times S_4\\times F_{11}', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 12, 'autcent_group': '48.48', 'autcent_hash': 48, 'autcent_nilpotent': False, 'autcent_order': 48, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2\\times S_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 11, 4], [3, 1, 2], [6, 1, 6], [6, 11, 8], [11, 2, 5], [22, 2, 15], [33, 2, 10], [66, 2, 30]], 'center_label': '12.5', 'center_order': 12, 'central_product': True, 'central_quotient': '22.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 36, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 2], ['22.1', 1], ['3.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 11, 1, 4], [3, 1, 2, 1], [6, 1, 2, 3], [6, 11, 2, 4], [11, 2, 5, 1], [22, 2, 5, 3], [33, 2, 10, 1], [66, 2, 10, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1092, 'exponent': 66, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 11], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '264.36', 'hash': 36, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 22, 'inner_gen_orders': [1, 2, 11], 'inner_gens': [[1, 2, 4], [1, 2, 172], [1, 98, 4]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 22, 'inner_split': True, 'inner_tex': 'D_{11}', 'inner_used': [2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 24], [2, 60]], 'label': '264.36', 'linC_count': 480, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 12, 'linQ_dim': 12, 'linQ_dim_count': 12, 'linR_count': 60, 'linR_degree': 4, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C6*D22', 'ngens': 5, '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': 10, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 84, 'number_divisions': 24, 'number_normal_subgroups': 42, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 64, 'number_subgroups': 284, 'old_label': None, 'order': 264, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 47], [3, 2], [6, 94], [11, 10], [22, 30], [33, 20], [66, 60]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 60, 'outer_gen_orders': [10, 10, 5, 2, 10, 15], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 135, 148], [1, 3, 68], [1, 2, 196], [132, 135, 41], [1, 2, 140], [132, 135, 125]], 'outer_group': '240.196', 'outer_hash': 196, 'outer_nilpotent': False, 'outer_order': 240, 'outer_permdeg': 11, 'outer_perms': [7984230, 11654209, 1728, 766080, 2521, 405720], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_{10}\\times S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 8], [10, 4], [20, 4]], 'representations': {'PC': {'code': 71718468195303600019, 'gens': [1, 2, 3], 'pres': [5, -2, -2, -2, -3, -11, 1297, 42, 808, 78, 3009]}, 'GLZN': {'d': 2, 'p': 33, 'gens': [826574, 359380, 36037, 36301, 826979]}, 'Perm': {'d': 18, 'gens': [21010450849920, 744, 1680, 3, 397708329755520]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 6], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_6\\times D_{22}', 'transitive_degree': 132, 'wreath_data': None, 'wreath_product': False}
