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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'ambient': '960.1217', 'ambient_counter': 1217, 'ambient_order': 960, 'ambient_tex': 'C_{12}:D_{40}', 'central': True, 'central_factor': False, 'centralizer_order': 960, 'characteristic': True, 'core_order': 2, 'counter': 262, 'cyclic': True, 'direct': False, 'hall': 0, 'label': '960.1217.480.b1.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': True, 'minimal_normal': True, 'nilpotent': True, 'normal': True, 'old_label': '480.b1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '480.519', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 519, 'quotient_metabelian': True, 'quotient_nilpotent': False, 'quotient_order': 480, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{12}:D_{20}', 'simple': True, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': True, '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': '960.1217', 'aut_centralizer_order': 30720, 'aut_label': '480.b1', 'aut_quo_index': 2, 'aut_stab_index': 1, 'aut_weyl_group': '1.1', 'aut_weyl_index': 30720, 'centralizer': '1.a1.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['96.b1.a1', '160.b1.a1', '240.a1.a1', '240.c1.a1', '240.d1.a1', '240.i1.a1', '240.i1.b1', '240.j1.a1', '240.j1.b1'], 'contains': ['960.a1.a1'], 'core': '480.b1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5518, 6397, 6462, 5047, 6765, 5461, 4131, 4502], 'generators': [40], 'label': '960.1217.480.b1.a1', 'mobius_quo': -1, 'mobius_sub': 0, 'normal_closure': '480.b1.a1', 'normal_contained_in': ['96.b1.a1', '160.b1.a1', '240.a1.a1', '240.d1.a1', '240.c1.a1'], 'normal_contains': ['960.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '480.b1.a1', 'projective_image': '480.519', 'quotient_action_image': '1.1', 'quotient_action_kernel': '480.519', 'quotient_action_kernel_order': 480, 'quotient_fusion': None, 'short_label': '480.b1.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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [10, 4, 4, 4, 4, 4, 12, 4, 4, 4], 'aut_gens': [[1, 2, 80], [69, 222, 400], [1, 686, 880], [497, 846, 440], [61, 162, 920], [553, 334, 400], [549, 18, 920], [37, 646, 560], [541, 494, 440], [497, 14, 440], [21, 486, 80]], 'aut_group': None, 'aut_hash': 7312598050044633167, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 30720, 'aut_permdeg': 68, 'aut_perms': [842227631888870970462782077408314011284881811449758435450512817475870584290135623158052296943385, 1443453361102436121130126050424207328149246898976702205848850013660147986759329136416262781814, 1889361656441009301244023867278250189312713392996886852294813921850861771844419096969458713592779, 72463975055061912094329243876290611573513652929777988108855676691990876714538551758511696488670, 108589595428068245867168366447083113165483757005600667995024080709298768331690751532197538222865, 1553827159721693617665295147116993839972206038809611891315483286495403542893058810772931624037633, 1400587208602369246968691507936530922992887425125027041518062375146108513551713357934329110368678, 592628217468861983902307093472466932767528019341938777680894462314572732480871065092716914920355, 1889419388164799818614373929980780172538059882633345933330527829643046498467087133653697632364338, 145744245119554388538305185497595562260189065110724272481198417681626911525380963353325444541887], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 20, 2, 1], [2, 60, 2, 1], [3, 2, 1, 1], [4, 1, 4, 1], [4, 2, 1, 2], [4, 2, 2, 1], [4, 20, 2, 1], [4, 60, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 20, 4, 1], [8, 6, 4, 2], [10, 2, 2, 3], [12, 2, 4, 1], [12, 4, 1, 2], [12, 4, 2, 1], [12, 20, 4, 1], [15, 4, 2, 1], [20, 2, 4, 2], [20, 2, 8, 2], [30, 4, 2, 3], [40, 6, 16, 2], [60, 4, 4, 2], [60, 4, 8, 2]], 'aut_supersolvable': True, 'aut_tex': 'C_{15}:(C_2^6\\times C_4\\times D_4)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': False, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '480.1197', 'autcentquo_hash': 1197, 'autcentquo_nilpotent': False, 'autcentquo_order': 480, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 20, 2], [2, 60, 2], [3, 2, 1], [4, 1, 4], [4, 2, 4], [4, 20, 2], [4, 60, 2], [5, 2, 2], [6, 2, 3], [6, 20, 4], [8, 6, 8], [10, 2, 6], [12, 2, 4], [12, 4, 4], [12, 20, 4], [15, 4, 2], [20, 2, 24], [30, 4, 6], [40, 6, 32], [60, 4, 24]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '120.12', 'commutator_count': 1, 'commutator_label': '60.4', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 1217, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['240.14', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 20, 1, 2], [2, 60, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 2, 1, 2], [4, 2, 2, 1], [4, 20, 2, 1], [4, 60, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 20, 2, 2], [8, 6, 2, 2], [8, 6, 4, 1], [10, 2, 2, 3], [12, 2, 2, 2], [12, 4, 1, 2], [12, 4, 2, 1], [12, 20, 4, 1], [15, 4, 2, 1], [20, 2, 4, 4], [20, 2, 8, 1], [30, 4, 2, 3], [40, 6, 8, 2], [40, 6, 16, 1], [60, 4, 4, 4], [60, 4, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 8064, 'exponent': 120, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '120.42', 'hash': 1217, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 60, 'inner_gen_orders': [2, 20, 3], 'inner_gens': [[1, 78, 80], [5, 2, 400], [1, 642, 80]], 'inner_hash': 12, 'inner_nilpotent': False, 'inner_order': 120, 'inner_split': True, 'inner_tex': 'C_3:D_{20}', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 92], [4, 36]], 'label': '960.1217', 'linC_count': 256, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 32, 'linQ_dim': 12, 'linQ_dim_count': 144, 'linR_count': 352, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12:D40', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 42, 'number_characteristic_subgroups': 64, 'number_conjugacy_classes': 144, 'number_divisions': 51, 'number_normal_subgroups': 86, 'number_subgroup_autclasses': 216, 'number_subgroup_classes': 268, 'number_subgroups': 2024, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 163], [3, 2], [4, 172], [5, 4], [6, 86], [8, 48], [10, 12], [12, 104], [15, 8], [20, 48], [30, 24], [40, 192], [60, 96]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 400], [1, 42, 80], [1, 2, 120], [481, 2, 80], [1, 482, 80], [1, 2, 560], [1, 34, 80]], 'outer_group': '256.56082', 'outer_hash': 56082, 'outer_nilpotent': True, 'outer_order': 256, 'outer_permdeg': 16, 'outer_perms': [362880, 1307674368000, 6227020800, 39916800, 5040, 120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^6\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 13], [8, 11], [16, 7], [32, 2]], 'representations': {'PC': {'code': 1440182963643579951923925723332739361664538640577, 'gens': [1, 2, 6], 'pres': [8, -2, -2, -2, -2, -5, -2, -2, -3, 1249, 41, 1826, 66, 2307, 91, 2564, 9613, 141, 22414, 166, 20495]}, 'GLZN': {'d': 2, 'p': 70, 'gens': [14211989, 19750527, 343981, 9947029, 2695417, 9261027, 516986, 23667069]}, 'Perm': {'d': 20, 'gens': [122398327071825960, 245152329121324800, 391971468784896009, 16, 519034357505664000, 391971468784896000, 43545600, 50520]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}:D_{40}', 'transitive_degree': 480, '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': '16.10', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 60, 'aut_gen_orders': [4, 2, 4, 2, 2, 2, 10, 2, 12], 'aut_gens': [[1, 2, 40], [241, 326, 220], [257, 258, 280], [249, 254, 40], [5, 178, 460], [9, 178, 460], [37, 258, 200], [17, 342, 460], [249, 418, 200], [261, 434, 280]], 'aut_group': None, 'aut_hash': 814302305876374217, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 7680, 'aut_permdeg': 36, 'aut_perms': [247076197478460384179466032271378991014567, 92402753874932909663662609500295227007651, 62602607559203412196143414179769754092178, 41939901908201274315395795297254762723438, 50753473292700457770470714008433235809908, 84199450817354845124150233791842823984092, 245244020363720531836422781496897020581627, 214861649124077516840493338088358475534788, 208197230707153705371991759343777566169522], 'aut_phi_ratio': 60.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 2, 1], [2, 30, 2, 1], [3, 2, 1, 1], [4, 1, 4, 1], [4, 6, 2, 2], [4, 10, 2, 1], [4, 30, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 10, 4, 1], [10, 2, 2, 3], [12, 2, 4, 1], [12, 10, 4, 1], [15, 4, 2, 1], [20, 2, 8, 1], [20, 6, 8, 2], [30, 4, 2, 3], [60, 4, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^6\\times S_3\\times F_5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '64.267', 'autcent_hash': 267, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^6', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 60, 'autcentquo_group': '120.36', 'autcentquo_hash': 36, 'autcentquo_nilpotent': False, 'autcentquo_order': 120, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_5', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 10, 2], [2, 30, 2], [3, 2, 1], [4, 1, 4], [4, 6, 4], [4, 10, 2], [4, 30, 2], [5, 2, 2], [6, 2, 3], [6, 10, 4], [10, 2, 6], [12, 2, 4], [12, 10, 4], [15, 4, 2], [20, 2, 8], [20, 6, 16], [30, 4, 6], [60, 4, 8]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '60.8', 'commutator_count': 1, 'commutator_label': '30.4', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '5.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 519, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['120.12', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 10, 1, 2], [2, 30, 1, 2], [3, 2, 1, 1], [4, 1, 2, 2], [4, 6, 1, 2], [4, 6, 2, 1], [4, 10, 2, 1], [4, 30, 2, 1], [5, 2, 2, 1], [6, 2, 1, 3], [6, 10, 2, 2], [10, 2, 2, 3], [12, 2, 2, 2], [12, 10, 4, 1], [15, 4, 2, 1], [20, 2, 4, 2], [20, 6, 4, 2], [20, 6, 8, 1], [30, 4, 2, 3], [60, 4, 4, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 4032, 'exponent': 60, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 5], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '120.42', 'hash': 519, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 30, 'inner_gen_orders': [2, 10, 3], 'inner_gens': [[1, 38, 40], [5, 2, 200], [1, 322, 40]], 'inner_hash': 8, 'inner_nilpotent': False, 'inner_order': 60, 'inner_split': True, 'inner_tex': 'S_3\\times D_5', 'inner_used': [1, 2, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 52], [4, 16]], 'label': '480.519', 'linC_count': 192, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 184, 'linQ_dim': 10, 'linQ_dim_count': 176, 'linR_count': 176, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C12:D20', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 30, 'number_characteristic_subgroups': 44, 'number_conjugacy_classes': 84, 'number_divisions': 39, 'number_normal_subgroups': 66, 'number_subgroup_autclasses': 144, 'number_subgroup_classes': 188, 'number_subgroups': 988, 'old_label': None, 'order': 480, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 83], [3, 2], [4, 108], [5, 4], [6, 46], [10, 12], [12, 48], [15, 8], [20, 112], [30, 24], [60, 32]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2, 2, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0], 'outer_gens': [[1, 2, 200], [241, 2, 40], [1, 242, 40], [1, 2, 60], [1, 2, 280], [1, 26, 40]], 'outer_group': '128.2319', 'outer_hash': 2319, 'outer_nilpotent': True, 'outer_order': 128, 'outer_permdeg': 14, 'outer_perms': [39916800, 6227020800, 362880, 5040, 120, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^5\\times C_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 10], [4, 9], [8, 9], [16, 3]], 'representations': {'PC': {'code': 2986818122736204565702951287222272193, 'gens': [1, 2, 5], 'pres': [7, -2, -2, -2, -5, -2, -2, -3, 533, 36, 758, 58, 899, 3511, 102, 8412, 124, 7853]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [136017, 110203, 92049, 72009, 8081, 24003, 130311]}, 'Perm': {'d': 16, 'gens': [87660962664, 3670585, 8026104, 3669120, 2424, 3, 1482509952000]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 4], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}:D_{20}', 'transitive_degree': 240, 'wreath_data': None, 'wreath_product': False}
