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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '176400.a', 'ambient_counter': 1, 'ambient_order': 176400, 'ambient_tex': 'C_{420}.D_{210}', 'central': False, 'central_factor': True, 'centralizer_order': None, 'characteristic': True, 'core_order': 17640, 'counter': 49, 'cyclic': False, 'direct': None, 'hall': 0, 'label': '176400.a.10._.H', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.H', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': None, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': [], 'split': None, 'standard_generators': False, 'stem': False, 'subgroup': '17640.h', 'subgroup_hash': None, 'subgroup_order': 17640, 'subgroup_tex': 'C_{21}\\times D_{420}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '176400.a', 'aut_centralizer_order': None, 'aut_label': None, 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': None, 'complements': None, 'conjugacy_class_count': 1, 'contained_in': None, 'contains': None, 'core': None, 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [27608830571, 3581686435, 15744495273, 23579433680, 9103452243, 5894858435, 177662, 2462409583], 'label': '176400.a.10._.H', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': None, 'normal_contained_in': None, 'normal_contains': None, 'normalizer': None, 'old_label': '10.H', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '10._.H', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '84.15', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 420, 'aut_gen_orders': [12, 2, 30, 12, 12, 30, 12, 210], 'aut_gens': [[1, 42], [13673, 9282], [461, 1722], [3527, 11382], [12401, 11046], [1993, 2226], [9413, 9282], [1487, 10374], [15641, 2982]], 'aut_group': None, 'aut_hash': 3193964801854808590, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 483840, 'aut_permdeg': 428, 'aut_perms': 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'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 210, 2, 1], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 210, 4, 1], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 18, 1], [10, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 18, 1], [14, 210, 12, 1], [15, 2, 4, 2], [15, 2, 8, 1], [20, 2, 4, 1], [21, 1, 12, 1], [21, 2, 6, 3], [21, 2, 12, 2], [21, 2, 36, 2], [21, 2, 72, 1], [28, 2, 6, 2], [28, 2, 36, 1], [30, 2, 4, 2], [30, 2, 8, 1], [35, 2, 12, 2], [35, 2, 72, 1], [42, 1, 12, 1], [42, 2, 6, 3], [42, 2, 12, 2], [42, 2, 36, 2], [42, 2, 72, 1], [42, 210, 24, 1], [60, 2, 8, 2], [60, 2, 16, 1], [70, 2, 12, 2], [70, 2, 72, 1], [84, 2, 12, 4], [84, 2, 24, 2], [84, 2, 72, 2], [84, 2, 144, 1], [105, 2, 24, 4], [105, 2, 48, 2], [105, 2, 144, 2], [105, 2, 288, 1], [140, 2, 24, 2], [140, 2, 144, 1], [210, 2, 24, 4], [210, 2, 48, 2], [210, 2, 144, 2], [210, 2, 288, 1], [420, 2, 48, 4], [420, 2, 96, 2], [420, 2, 288, 2], [420, 2, 576, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{35}.C_6^3.C_2^6', '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': 420, 'autcentquo_group': None, 'autcentquo_hash': 2285439238770837057, 'autcentquo_nilpotent': False, 'autcentquo_order': 10080, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times F_5\\times S_3\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 210, 2], [3, 1, 2], [3, 2, 3], [4, 2, 1], [5, 2, 2], [6, 1, 2], [6, 2, 3], [6, 210, 4], [7, 1, 6], [7, 2, 21], [10, 2, 2], [12, 2, 8], [14, 1, 6], [14, 2, 21], [14, 210, 12], [15, 2, 16], [20, 2, 4], [21, 1, 12], [21, 2, 186], [28, 2, 48], [30, 2, 16], [35, 2, 96], [42, 1, 12], [42, 2, 186], [42, 210, 24], [60, 2, 32], [70, 2, 96], [84, 2, 384], [105, 2, 768], [140, 2, 192], [210, 2, 768], [420, 2, 1536]], 'center_label': '42.6', 'center_order': 42, 'central_product': True, 'central_quotient': '420.40', 'commutator_count': None, 'commutator_label': '210.12', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '3.1', '3.1', '5.1', '7.1', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 8, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['3.1', 1], ['7.1', 1], ['840.128', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 210, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 2, 1, 1], [5, 2, 2, 1], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 1], [6, 210, 2, 2], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 6, 3], [10, 2, 2, 1], [12, 2, 2, 2], [12, 2, 4, 1], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 6, 3], [14, 210, 6, 2], [15, 2, 4, 2], [15, 2, 8, 1], [20, 2, 4, 1], [21, 1, 12, 1], [21, 2, 6, 3], [21, 2, 12, 14], [28, 2, 6, 2], [28, 2, 12, 3], [30, 2, 4, 2], [30, 2, 8, 1], [35, 2, 12, 2], [35, 2, 24, 3], [42, 1, 12, 1], [42, 2, 6, 3], [42, 2, 12, 14], [42, 210, 12, 2], [60, 2, 8, 2], [60, 2, 16, 1], [70, 2, 12, 2], [70, 2, 24, 3], [84, 2, 12, 4], [84, 2, 24, 14], [105, 2, 24, 4], [105, 2, 48, 14], [140, 2, 24, 2], [140, 2, 48, 3], [210, 2, 24, 4], [210, 2, 48, 14], [420, 2, 48, 4], [420, 2, 96, 14]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 96, 'exponent': 420, 'exponents_of_order': [3, 2, 2, 1], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '8820.b', 'hash': 3250163271357678442, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 210, 'inner_gen_orders': [2, 210], 'inner_gens': [[1, 17598], [85, 42]], 'inner_hash': 40, 'inner_nilpotent': False, 'inner_order': 420, 'inner_split': True, 'inner_tex': 'D_{210}', 'inner_used': [1, 2], 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '17640.h', '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': True, 'monomial': True, 'name': 'C21*D420', '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, 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': 100, 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'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^4\times C_6\times C_{12}', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 29, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 3, 7], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '842070803812813901038798878430727442664347312550914546444635', 'gens': [1, 4], 'pres': [8, -2, -3, -7, -2, -2, -3, -5, -7, 16, 57, 563139, 91, 702244, 116, 838661, 189, 959622, 334, 967687]}, 'GLFp': {'d': 2, 'p': 421, 'gens': [15744495273, 21340879847, 177662]}, 'Perm': {'d': 29, 'gens': [316583823960402890602770260251, 22584322947090643371309600475, 51706594805170137237161]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 42], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{21}\\times D_{420}', 'transitive_degree': 840, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '840.186', 'all_subgroups_known': False, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[298473845, 15744495273, 177662], [298473845, 15744495273, 74618040], [74618465, 149237133, 177662], [298473845, 15744495273, 177662], [298473845, 15744495273, 177662], [298473845, 15744495273, 177662], [298473845, 15744495273, 177662], [298473845, 15744495273, 177662], [298473845, 15744495273, 70904820], [298473845, 15744495273, 49556331], [298473845, 15744495273, 13397062], [13953652592, 30071240087, 177662], [25295658587, 11491243374, 177662], [31339754037, 31265135369, 177662], [31339754037, 149237133, 177662], [20072366243, 31265135369, 177662], [17236864573, 31265135369, 177662], [23579433677, 31265135369, 177662], [31339754037, 31265135369, 5305021]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 3870720, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': 96.0, 'aut_solvable': None, 'aut_stats': None, 'aut_supersolvable': None, 'aut_tex': None, 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 1], [2, 210, 2], [3, 1, 2], [3, 2, 3], [4, 1, 2], [4, 2, 1], [4, 210, 2], [5, 1, 4], [5, 2, 10], [6, 1, 2], [6, 2, 11], [6, 210, 4], [7, 1, 6], [7, 2, 21], [10, 1, 4], [10, 2, 34], [10, 210, 8], [12, 1, 4], [12, 2, 14], [12, 210, 4], [14, 1, 6], [14, 2, 69], [14, 210, 12], [15, 1, 8], [15, 2, 92], [20, 1, 8], [20, 2, 44], [20, 210, 8], [21, 1, 12], [21, 2, 186], [28, 1, 12], [28, 2, 90], [28, 210, 12], [30, 1, 8], [30, 2, 284], [30, 210, 16], [35, 1, 24], [35, 2, 564], [42, 1, 12], [42, 2, 570], [42, 210, 24], [60, 1, 16], [60, 2, 376], [60, 210, 16], [70, 1, 24], [70, 2, 1716], [70, 210, 48], [84, 1, 24], [84, 2, 756], [84, 210, 24], [105, 1, 48], [105, 2, 4584], [140, 1, 48], [140, 2, 2280], [140, 210, 48], [210, 1, 48], [210, 2, 13800], [210, 210, 96], [420, 1, 96], [420, 2, 18384], [420, 210, 96]], 'center_label': '420.12', 'center_order': 420, 'central_product': True, 'central_quotient': '420.40', 'commutator_count': None, 'commutator_label': '210.12', 'complements_known': False, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '5.1', '5.1', '7.1', '7.1'], 'composition_length': 10, 'conjugacy_classes_known': False, 'counter': 1, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['1680.913', 1], ['3.1', 1], ['5.1', 1], ['7.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 1], [2, 210, 1, 2], [3, 1, 2, 1], [3, 2, 1, 1], [3, 2, 2, 1], [4, 1, 2, 1], [4, 2, 1, 1], [4, 210, 1, 2], [5, 1, 4, 1], [5, 2, 2, 1], [5, 2, 4, 2], [6, 1, 2, 1], [6, 2, 1, 1], [6, 2, 2, 5], [6, 210, 2, 2], [7, 1, 6, 1], [7, 2, 3, 1], [7, 2, 6, 3], [10, 1, 4, 1], [10, 2, 2, 1], [10, 2, 4, 8], [10, 210, 4, 2], [12, 1, 4, 1], [12, 2, 2, 3], [12, 2, 4, 2], [12, 210, 2, 2], [14, 1, 6, 1], [14, 2, 3, 1], [14, 2, 6, 11], [14, 210, 6, 2], [15, 1, 8, 1], [15, 2, 4, 3], [15, 2, 8, 10], [20, 1, 8, 1], [20, 2, 4, 3], [20, 2, 8, 4], [20, 210, 4, 2], [21, 1, 12, 1], [21, 2, 6, 3], [21, 2, 12, 14], [28, 1, 12, 1], [28, 2, 6, 3], [28, 2, 12, 6], [28, 210, 6, 2], [30, 1, 8, 1], [30, 2, 4, 3], [30, 2, 8, 34], [30, 210, 8, 2], [35, 1, 24, 1], [35, 2, 12, 3], [35, 2, 24, 22], [42, 1, 12, 1], [42, 2, 6, 3], [42, 2, 12, 46], [42, 210, 12, 2], [60, 1, 16, 1], [60, 2, 8, 7], [60, 2, 16, 20], [60, 210, 8, 2], [70, 1, 24, 1], [70, 2, 12, 3], [70, 2, 24, 70], [70, 210, 24, 2], [84, 1, 24, 1], [84, 2, 12, 7], [84, 2, 24, 28], [84, 210, 12, 2], [105, 1, 48, 1], [105, 2, 24, 7], [105, 2, 48, 92], [140, 1, 48, 1], [140, 2, 24, 7], [140, 2, 48, 44], [140, 210, 24, 2], [210, 1, 48, 1], [210, 2, 24, 7], [210, 2, 48, 284], [210, 210, 48, 2], [420, 1, 96, 1], [420, 2, 48, 15], [420, 2, 96, 184], [420, 210, 48, 2]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': None, 'exponent': 420, 'exponents_of_order': [4, 2, 2, 2], 'factors_of_aut_order': [2, 3, 5, 7], 'factors_of_order': [2, 3, 5, 7], 'faithful_reps': None, 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': None, 'hash': 4653415526737240122, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': [210, 210, 2], 'inner_gens': [[298473845, 15744495273, 56009840], [298473845, 15744495273, 842000], [74618465, 149237133, 177662]], 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 420, 'inner_split': None, 'inner_tex': 'D_{210}', 'inner_used': None, 'irrC_degree': None, 'irrQ_degree': None, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': None, 'label': '176400.a', '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': 'C420.D210', 'ngens': 3, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [1, 1, 2, 3, 2, 2, 2, 1, 1, 2, 6, 2, 4, 0, 1, 6, 4, 2, 1, 6, 4, 4, 3, 2, 4, 2, 0, 1, 1, 2, 12, 2, 4, 1, 2, 0, 12, 2, 1, 3, 8, 0, 4, 2, 12, 0, 2, 2, 4, 2, 6, 3, 1, 8, 1, 0, 2, 6, 4, 2, 6, 4, 0, 2, 2, 1, 0, 28, 1, 1, 2, 2, 4, 0, 6, 2, 4, 6, 0, 4, 0, 14, 1, 3, 6, 0, 4, 2, 0, 1, 16, 2, 4, 2, 1, 3, 1, 2, 16, 2, 0, 1, 10, 0, 16, 2, 1, 0, 2, 0, 10, 2, 3, 1, 10, 10, 0, 2, 1, 10, 1, 1, 1, 8, 10, 8, 0, 1, 1, 8, 1, 7, 1, 7, 1], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': None, 'number_characteristic_subgroups': 408, 'number_conjugacy_classes': 44730, 'number_divisions': 1031, 'number_normal_subgroups': 472, 'number_subgroup_autclasses': None, 'number_subgroup_classes': None, 'number_subgroups': None, 'old_label': None, 'order': 176400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 423], [3, 8], [4, 424], [5, 24], [6, 864], [7, 48], [10, 1752], [12, 872], [14, 2664], [15, 192], [20, 1776], [21, 384], [28, 2712], [30, 3936], [35, 1152], [42, 6192], [60, 4128], [70, 13536], [84, 6576], [105, 9216], [140, 14688], [210, 47808], [420, 57024]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': False, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': None, 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 9216, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': None, 'pc_rank': 3, 'perfect': False, 'permutation_degree': 38, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 3, 5, 7], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': None, 'representations': {'PC': {'code': '66798095205065271706105589258719621828377411305165747097779040050581298378930267', 'gens': [1, 2, 6], 'pres': [10, -2, -2, -3, -5, -7, -2, -2, -3, -5, -7, 2276361, 51, 1524482, 112, 6064323, 233, 2538004, 175, 206, 317, 538]}, 'GLFp': {'d': 2, 'p': 421, 'gens': [298473845, 15744495273, 177662]}, 'Perm': {'d': 38, 'gens': [14508035248958862673264279215927571938362091, 372288567811779475786769890909425273909890, 27548173004656294208510449541784083277995130]}}, 'schur_multiplier': None, 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 210], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': False, 'subgroup_index_bound': 252, 'supersolvable': True, 'sylow_subgroups_known': False, 'tex_name': 'C_{420}.D_{210}', 'transitive_degree': None, 'wreath_data': None, 'wreath_product': None}
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [7]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4], [10, 1, 4]], 'center_label': '10.2', 'center_order': 10, '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', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 10]], 'label': '10.2', 'linC_count': 4, 'linC_degree': 1, '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': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C10', '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': 10, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[7]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2]], 'representations': {'PC': {'code': 83, 'gens': [1], 'pres': [2, -2, -5, 4]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504]}, 'Perm': {'d': 7, 'gens': [720, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}
