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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47365', 'ambient_counter': 47365, 'ambient_order': 1728, 'ambient_tex': 'Q_8:S_3^3', 'central': False, 'central_factor': False, 'centralizer_order': 24, 'characteristic': False, 'core_order': 36, 'counter': 487, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47365.48.l1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '48.l1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '48.51', 'quotient_Agroup': True, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 51, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 48, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2\\times D_6', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '36.7', 'subgroup_hash': 7, 'subgroup_order': 36, 'subgroup_tex': 'C_3^2:C_4', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.47365', 'aut_centralizer_order': None, 'aut_label': '48.l1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '72.b1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['16.j1', '24.e1', '24.k1', '24.s1', '24.u1', '24.bo1', '24.br1', '24.cz1', '24.dd1', '24.dp1'], 'contains': ['96.b1', '144.bb1', '144.bn1'], 'core': '48.l1', 'coset_action_label': None, 'count': 3, 'diagramx': None, 'generators': [1299, 864, 4, 48], 'label': '1728.47365.48.l1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '48.l1', 'normal_contained_in': ['16.j1', '24.e1', '24.k1', '24.s1', '24.u1'], 'normal_contains': ['96.b1'], 'normalizer': '1.a1', 'old_label': '48.l1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '48.l1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 5, 'aut_exponent': 24, 'aut_gen_orders': [2, 4, 2, 4, 3, 2, 6, 6], 'aut_gens': [[1, 4, 12], [3, 4, 12], [23, 28, 32], [25, 8, 24], [19, 16, 28], [9, 4, 12], [1, 32, 12], [19, 4, 12], [11, 20, 24]], 'aut_group': '864.4661', 'aut_hash': 4661, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 864, 'aut_permdeg': 11, 'aut_perms': [1, 10889689, 24054000, 20507935, 14605950, 2245249, 19496545, 16180705], 'aut_phi_ratio': 72.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 4, 1], [4, 9, 2, 1], [6, 2, 4, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2\\times C_3^2:\\GL(2,3)', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '432.734', 'autcentquo_hash': 734, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^2:\\GL(2,3)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [3, 2, 4], [4, 9, 2], [6, 2, 4]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '18.4', 'commutator_count': 1, 'commutator_label': '9.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '3.1', '3.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 7, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [3, 2, 1, 4], [4, 9, 2, 1], [6, 2, 1, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 28, 'exponent': 12, 'exponents_of_order': [2, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '18.4', 'hash': 7, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3], 'inner_gens': [[1, 8, 24], [9, 4, 12], [25, 4, 12]], 'inner_hash': 4, 'inner_nilpotent': False, 'inner_order': 18, 'inner_split': False, 'inner_tex': 'C_3:S_3', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 4], [2, 8]], 'label': '36.7', 'linC_count': 18, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 18, 'linQ_dim': 6, 'linQ_dim_count': 18, 'linR_count': 18, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C3^2:C4', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 12, 'number_divisions': 11, 'number_normal_subgroups': 13, 'number_subgroup_autclasses': 9, 'number_subgroup_classes': 18, 'number_subgroups': 34, 'old_label': None, 'order': 36, 'order_factorization_type': 22, 'order_stats': [[1, 1], [2, 1], [3, 8], [4, 18], [6, 8]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 3, 2, 2], 'outer_gen_pows': [0, 0, 0, 1, 1], 'outer_gens': [[3, 24, 8], [3, 4, 12], [1, 24, 28], [1, 32, 20], [1, 20, 16]], 'outer_group': '48.48', 'outer_hash': 48, 'outer_nilpotent': False, 'outer_order': 48, 'outer_permdeg': 6, 'outer_perms': [143, 127, 576, 126, 121], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2\\times S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 10, 'pgroup': 0, 'primary_abelian_invariants': [4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9]], 'representations': {'PC': {'code': 11576083, 'gens': [1, 3, 4], 'pres': [4, -2, -2, -3, -3, 8, 98, 387]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [125124616718753647, 58415899998881273, 125101736062734304]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [11689448, 17625105, 28816400, 37924170]}, 'Perm': {'d': 10, 'gens': [41185, 1680, 403203, 3]}}, 'schur_multiplier': [3], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3^2:C_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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [6, 12, 4, 2, 12, 6, 2], 'aut_gens': [[1, 2, 12, 24, 144], [54, 97, 444, 800, 588], [1, 970, 1296, 1140, 1452], [870, 105, 444, 220, 1584], [1, 922, 876, 120, 156], [9, 914, 444, 744, 720], [5, 922, 432, 756, 1596], [9, 10, 12, 1176, 720]], 'aut_group': None, 'aut_hash': 942252590584195724, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 82944, 'aut_permdeg': 24, 'aut_perms': [152297894689764724364505, 19191514483363089751212, 466055521751745882620510, 2299786626428730910153, 564183427232389608877075, 278481055957010281196649, 545044274773266031154220], 'aut_phi_ratio': 144.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 4, 1], [2, 6, 3, 1], [2, 9, 2, 1], [2, 18, 6, 1], [2, 54, 3, 1], [3, 2, 1, 1], [3, 2, 2, 1], [3, 4, 1, 1], [3, 4, 2, 1], [3, 8, 1, 1], [4, 2, 3, 1], [4, 3, 2, 1], [4, 6, 6, 1], [4, 9, 4, 1], [4, 18, 3, 1], [4, 27, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 4, 1, 1], [6, 4, 2, 1], [6, 6, 4, 2], [6, 8, 1, 1], [6, 12, 4, 1], [6, 12, 6, 1], [6, 18, 2, 1], [6, 24, 3, 1], [6, 36, 6, 1], [12, 4, 3, 1], [12, 4, 6, 1], [12, 6, 4, 1], [12, 8, 3, 1], [12, 8, 6, 1], [12, 12, 2, 1], [12, 12, 6, 2], [12, 16, 3, 1], [12, 18, 4, 1], [12, 24, 6, 1], [12, 36, 3, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^2.C_6^2.C_2^6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '32.51', 'autcent_hash': 51, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '2592.fs', 'autcentquo_hash': 3641402233686599739, 'autcentquo_nilpotent': False, 'autcentquo_order': 2592, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'S_3^4:C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 4], [2, 6, 3], [2, 9, 2], [2, 18, 6], [2, 54, 3], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 2, 3], [4, 3, 2], [4, 6, 6], [4, 9, 4], [4, 18, 3], [4, 27, 2], [6, 2, 3], [6, 4, 3], [6, 6, 8], [6, 8, 1], [6, 12, 10], [6, 18, 2], [6, 24, 3], [6, 36, 6], [12, 4, 9], [12, 6, 4], [12, 8, 9], [12, 12, 14], [12, 16, 3], [12, 18, 4], [12, 24, 6], [12, 36, 3]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '864.4704', 'commutator_count': 1, 'commutator_label': '54.15', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 47365, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['48.41', 1], ['6.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 4], [2, 6, 1, 3], [2, 9, 1, 2], [2, 18, 1, 6], [2, 54, 1, 3], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 1, 3], [4, 3, 2, 1], [4, 6, 1, 6], [4, 9, 2, 2], [4, 18, 1, 3], [4, 27, 2, 1], [6, 2, 1, 3], [6, 4, 1, 3], [6, 6, 1, 8], [6, 8, 1, 1], [6, 12, 1, 10], [6, 18, 1, 2], [6, 24, 1, 3], [6, 36, 1, 6], [12, 4, 1, 9], [12, 6, 2, 2], [12, 8, 1, 9], [12, 12, 1, 12], [12, 12, 2, 1], [12, 16, 1, 3], [12, 18, 2, 2], [12, 24, 1, 6], [12, 36, 1, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 53329920000, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[16, 1, 1]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4704', 'hash': 47365, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 6, 2, 6, 6], 'inner_gens': [[1, 10, 12, 24, 144], [5, 2, 12, 120, 144], [1, 2, 12, 24, 1008], [1, 50, 12, 24, 1584], [1, 2, 876, 312, 144]], 'inner_hash': 4704, 'inner_nilpotent': False, 'inner_order': 864, 'inner_split': True, 'inner_tex': 'S_3\\times D_6^2', 'inner_used': [1, 2, 3, 4, 5], 'irrC_degree': 16, 'irrQ_degree': 16, 'irrQ_dim': 32, 'irrR_degree': 16, 'irrep_stats': [[1, 32], [2, 56], [4, 36], [8, 10], [16, 1]], 'label': '1728.47365', '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': True, 'metacyclic': False, 'monomial': True, 'name': 'Q8:S3^3', 'ngens': 9, '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 32, 'number_conjugacy_classes': 135, 'number_divisions': 126, 'number_normal_subgroups': 664, 'number_subgroup_autclasses': 864, 'number_subgroup_classes': 4092, 'number_subgroups': 30756, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 319], [3, 26], [4, 192], [6, 518], [12, 672]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 2, 2, 2, 3], 'outer_gen_pows': [12, 0, 7, 0, 0, 7], 'outer_gens': [[1, 2, 12, 120, 1596], [1, 2, 876, 120, 720], [6, 97, 876, 940, 720], [865, 2, 876, 120, 720], [865, 866, 12, 24, 720], [1, 10, 432, 1428, 1020]], 'outer_group': '96.209', 'outer_hash': 209, 'outer_nilpotent': False, 'outer_order': 96, 'outer_permdeg': 9, 'outer_perms': [5040, 143, 21, 136, 23, 80640], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4\\times D_6', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 17, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 48], [4, 32], [8, 12], [16, 2]], 'representations': {'PC': {'code': 6391719674496748598971563130793809448715173835076777033, 'gens': [1, 2, 4, 5, 7], 'pres': [9, -2, -2, -3, -2, -2, -3, -2, -2, -3, 181, 46, 218, 2622, 2713, 130, 2606, 5325, 4200, 186, 4363, 214, 3932]}, 'Perm': {'d': 17, 'gens': [21109604140936, 21109604140943, 45787363781040, 68355447955200, 86325272812800, 21109604140800, 325, 435, 45360]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'Q_8:S_3^3', 'transitive_degree': 96, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 84, 'aut_gen_orders': [14, 4], 'aut_gens': [[41041, 90720, 24, 131784, 3], [2, 131760, 90744, 41040, 4], [29, 41040, 131784, 90720, 4]], 'aut_group': '8064.bp', 'aut_hash': 8982001159746026648, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8064, 'aut_permdeg': 11, 'aut_perms': [26573066, 11017685], 'aut_phi_ratio': 504.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 7, 1], [2, 3, 8, 1], [3, 2, 1, 1], [6, 2, 7, 1]], 'aut_supersolvable': False, 'aut_tex': 'S_3\\times C_2^3:\\GL(3,2)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 84, 'autcent_group': '1344.11686', 'autcent_hash': 11686, 'autcent_nilpotent': False, 'autcent_order': 1344, 'autcent_solvable': False, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^3:\\GL(3,2)', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '6.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 6, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3', 'cc_stats': [[1, 1, 1], [2, 1, 7], [2, 3, 8], [3, 2, 1], [6, 2, 7]], 'center_label': '8.5', 'center_order': 8, 'central_product': True, 'central_quotient': '6.1', 'commutator_count': 1, 'commutator_label': '3.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 51, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 3], ['6.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [2, 3, 1, 8], [3, 2, 1, 1], [6, 2, 1, 7]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 195, 'exponent': 6, 'exponents_of_order': [4, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '48.51', 'hash': 51, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 1, 1, 1, 3], 'inner_gens': [[41041, 90720, 24, 131784, 4], [41041, 90720, 24, 131784, 3], [41041, 90720, 24, 131784, 3], [41041, 90720, 24, 131784, 3], [41045, 90720, 24, 131784, 3]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 6, 'inner_split': True, 'inner_tex': 'S_3', 'inner_used': [1, 5], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 8]], 'label': '48.51', 'linC_count': None, 'linC_degree': None, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': None, 'linQ_dim': None, 'linQ_dim_count': None, 'linR_count': None, 'linR_degree': None, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2^2*D6', 'ngens': 5, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 5, 'number_characteristic_subgroups': 5, 'number_conjugacy_classes': 24, 'number_divisions': 24, 'number_normal_subgroups': 83, 'number_subgroup_autclasses': 16, 'number_subgroup_classes': 134, 'number_subgroups': 236, 'old_label': None, 'order': 48, 'order_factorization_type': 31, 'order_stats': [[1, 1], [2, 31], [3, 2], [6, 14]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 84, 'outer_gen_orders': [4, 4], 'outer_gen_pows': [0, 0], 'outer_gens': [[41065, 90720, 41040, 41064, 3], [41041, 90744, 24, 41040, 3]], 'outer_group': '1344.11686', 'outer_hash': 11686, 'outer_nilpotent': False, 'outer_order': 1344, 'outer_permdeg': 8, 'outer_perms': [4498, 25112], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^3:\\GL(3,2)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 9, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8]], 'representations': {'PC': {'code': 1259012353, 'gens': [1, 2, 3, 4], 'pres': [5, -2, -2, -2, -2, -3, 213, 58, 214]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [7115648, 35813302, 7233337, 35931072]}, 'GLFp': {'d': 4, 'p': 3, 'gens': [6594100, 8188666, 16002800, 28816400, 17616532]}, 'Perm': {'d': 9, 'gens': [41041, 90720, 24, 131784, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2, 2], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2\\times D_6', 'transitive_degree': 24, 'wreath_data': None, 'wreath_product': False}
