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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1568.847', 'ambient_counter': 847, 'ambient_order': 1568, 'ambient_tex': 'C_2.D_{14}^2', 'central': False, 'central_factor': True, 'centralizer_order': 4, 'characteristic': False, 'core_order': 784, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '1568.847.2.e1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '2.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 2, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2', 'simple': False, 'solvable': True, 'special_labels': ['C1'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '784.121', 'subgroup_hash': 121, 'subgroup_order': 784, 'subgroup_tex': 'C_{28}.D_{14}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1568.847', 'aut_centralizer_order': 2, 'aut_label': '2.e1', 'aut_quo_index': 1, 'aut_stab_index': 8, 'aut_weyl_group': None, 'aut_weyl_index': 16, 'centralizer': '392.a1', 'complements': ['784.a1', '784.c1'], 'conjugacy_class_count': 8, 'contained_in': ['1.a1'], 'contains': ['4.e1', '4.f1', '4.g1', '4.h1', '14.g1'], 'core': '2.e1', 'coset_action_label': None, 'count': 8, 'diagramx': [6686, 5057, 6315, 4519], 'generators': [1, 224, 392, 784, 2, 8], 'label': '1568.847.2.e1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.e1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.e1', '4.f1', '4.g1', '4.h1'], 'normalizer': '1.a1', 'old_label': '2.e1', 'projective_image': '784.169', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.e1', 'subgroup_fusion': None, 'weyl_group': '392.41'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [4, 12, 12, 12, 4, 6], 'aut_gens': [[1, 2, 28], [518, 573, 212], [742, 513, 208], [182, 629, 608], [209, 90, 140], [322, 421, 600], [413, 410, 84]], 'aut_group': None, 'aut_hash': 6118215623095209897, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 56448, 'aut_permdeg': 56, 'aut_perms': [167269989548704686474815631182370593732502506688989050010054338275736026464, 185043258890251441409149016201252028612080545714206141750588582299485487745, 420877469835637446582979808205837514630112159870837126661231092639853104726, 557200367105620791462991348340434099171516359887553891501593317719614846366, 265693948021235193449750641210024715866457501669126789518224636046600215890, 360819272961909373887588765630695987066698185612319899239497103074345574416], 'aut_phi_ratio': 168.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 49, 2, 1], [4, 2, 1, 1], [4, 14, 4, 1], [4, 98, 1, 1], [7, 2, 6, 1], [7, 4, 9, 1], [14, 2, 6, 1], [14, 4, 9, 1], [28, 4, 6, 1], [28, 4, 18, 1], [28, 28, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_7^2.C_6^2.C_2^5', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '8.5', 'autcent_hash': 5, 'autcent_nilpotent': True, 'autcent_order': 8, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '7056.bg', 'autcentquo_hash': 7944870934666851665, 'autcentquo_nilpotent': False, 'autcentquo_order': 7056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_7^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 49, 2], [4, 2, 1], [4, 14, 4], [4, 98, 1], [7, 2, 6], [7, 4, 9], [14, 2, 6], [14, 4, 9], [28, 4, 24], [28, 28, 12]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '392.41', 'commutator_count': 1, 'commutator_label': '98.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '7.1', '7.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 121, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 49, 1, 2], [4, 2, 1, 1], [4, 14, 1, 4], [4, 98, 1, 1], [7, 2, 3, 2], [7, 4, 3, 3], [14, 2, 3, 2], [14, 4, 3, 3], [28, 4, 3, 2], [28, 4, 6, 3], [28, 28, 3, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2688, 'exponent': 28, 'exponents_of_order': [4, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [[4, 0, 18]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '392.41', 'hash': 121, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 14, 14], 'inner_gens': [[1, 26, 420], [397, 2, 756], [393, 58, 28]], 'inner_hash': 41, 'inner_nilpotent': False, 'inner_order': 392, 'inner_split': False, 'inner_tex': 'D_7\\times D_{14}', 'inner_used': [1, 2, 3], 'irrC_degree': 4, 'irrQ_degree': 24, 'irrQ_dim': 24, 'irrR_degree': 8, 'irrep_stats': [[1, 8], [2, 26], [4, 42]], 'label': '784.121', 'linC_count': 18, 'linC_degree': 4, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 14, 'linQ_degree_count': 44, 'linQ_dim': 16, 'linQ_dim_count': 44, 'linR_count': 333, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C28.D14', 'ngens': 6, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [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': 13, 'number_characteristic_subgroups': 10, 'number_conjugacy_classes': 76, 'number_divisions': 29, 'number_normal_subgroups': 34, 'number_subgroup_autclasses': 45, 'number_subgroup_classes': 100, 'number_subgroups': 976, 'old_label': None, 'order': 784, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 99], [4, 156], [7, 48], [14, 48], [28, 432]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6, 6], 'outer_gen_pows': [0, 15, 196, 0], 'outer_gens': [[393, 26, 420], [14, 617, 600], [197, 206, 140], [1, 398, 532]], 'outer_group': '144.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 144, 'outer_permdeg': 12, 'outer_perms': [40279680, 127370886, 87096961, 127370928], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6^2:C_2^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [6, 8], [12, 8], [24, 3]], 'representations': {'PC': {'code': 21493350012541130726170400293758822485501, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -7, -2, -2, -7, 2352, 313, 31, 7490, 1778, 10083, 9081, 69, 10930, 88, 12107]}, 'Perm': {'d': 22, 'gens': [101671758847, 2439325406344014720, 194163338880, 288848891520, 55969571858264064000, 973]}}, 'schur_multiplier': [2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [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_{28}.D_{14}', 'transitive_degree': 56, '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': '16.14', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 84, 'aut_gen_orders': [12, 6, 6, 6, 28, 12, 12], 'aut_gens': [[1, 2, 4, 56], [807, 386, 1484, 424], [1205, 834, 52, 168], [589, 586, 52, 1400], [1233, 494, 44, 728], [39, 374, 364, 1228], [835, 694, 1260, 1196], [1, 14, 828, 308]], 'aut_group': None, 'aut_hash': 8829740922017707739, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 903168, 'aut_permdeg': 112, 'aut_perms': [53319834826267575512171683867758868567312177798024935947701688165187210680869943305050666574809976865673778619352800249270041473762808758388842321575603861744005347760319705362015628, 81820530351837225133290923558454029665356824766860754441876626666058243505896543778706385551584814496437101164561566623899700815205188518772857213239392917574455788417836615921642419, 151369001143084664019595640694376669910150648642522392517095834898486249235076315395911757960742863024691144874981310683277426466755763441861276319844695177039041883515832050858236612, 183055176336500654960586589481519118353549068156481052929293084482024722686755273809319707855127533343734183917736088948189061526580353438488113569286377063278105435023476956919284673, 190550458614554644734627248075220545884886867140789846393545241123697222154284531403694651172917113377848582162787649205635080624683144297330058247216378088012895362170932542924829520, 143594384039068430705854285567063228675497059472236511493112653135856712833470358102215976410324704836228594728362162497222640048335478708385816814247094545147195473259026618626592089, 1198562970863591131413739995269368677688308422027070738801554707211076780726416269636617850428960879846022035781393838807230707903313602800545553293501451085507852165060314143575340], 'aut_phi_ratio': 1344.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 49, 4, 1], [4, 2, 2, 1], [4, 14, 8, 1], [4, 98, 2, 1], [7, 2, 6, 1], [7, 4, 9, 1], [14, 2, 6, 1], [14, 2, 12, 1], [14, 4, 9, 1], [14, 4, 18, 1], [28, 4, 12, 1], [28, 4, 36, 1], [28, 28, 24, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_7:D_7:C_3.C_2^4.C_6.C_2^5', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '128.1578', 'autcent_hash': 1578, 'autcent_nilpotent': True, 'autcent_order': 128, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 84, 'autcentquo_group': '7056.bg', 'autcentquo_hash': 7944870934666851665, 'autcentquo_nilpotent': False, 'autcentquo_order': 7056, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_7^2:C_2^2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 49, 4], [4, 2, 2], [4, 14, 8], [4, 98, 2], [7, 2, 6], [7, 4, 9], [14, 2, 18], [14, 4, 27], [28, 4, 48], [28, 28, 24]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '392.41', 'commutator_count': 1, 'commutator_label': '98.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '7.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 847, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['784.121', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 49, 1, 4], [4, 2, 1, 2], [4, 14, 1, 8], [4, 98, 1, 2], [7, 2, 3, 2], [7, 4, 3, 3], [14, 2, 3, 6], [14, 4, 3, 9], [28, 4, 3, 4], [28, 4, 6, 6], [28, 28, 3, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 2046870, 'exponent': 28, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '784.169', 'hash': 847, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 14, 'inner_gen_orders': [2, 2, 7, 14], 'inner_gens': [[1, 2, 4, 1512], [1, 2, 52, 728], [1, 10, 4, 56], [113, 898, 4, 56]], 'inner_hash': 41, 'inner_nilpotent': False, 'inner_order': 392, 'inner_split': False, 'inner_tex': 'D_7\\times D_{14}', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 52], [4, 84]], 'label': '1568.847', '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': 'C2.D14^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 12, 'number_conjugacy_classes': 152, 'number_divisions': 58, 'number_normal_subgroups': 124, 'number_subgroup_autclasses': 90, 'number_subgroup_classes': 393, 'number_subgroups': 4302, 'old_label': None, 'order': 1568, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 199], [4, 312], [7, 48], [14, 144], [28, 864]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [6, 12, 6, 12, 12, 4], 'outer_gen_pows': [0, 0, 2, 0, 0, 0], 'outer_gens': [[29, 814, 12, 532], [3, 2, 1036, 1228], [31, 2, 1372, 1192], [815, 814, 476, 1192], [393, 814, 44, 756], [815, 814, 140, 436]], 'outer_group': None, 'outer_hash': 6889544333894396836, 'outer_nilpotent': False, 'outer_order': 2304, 'outer_permdeg': 22, 'outer_perms': [372746951682308501783, 161186202261478518606, 371694682971401760, 260347191438234701663, 321534364415938249816, 372612857515692917777], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': '(C_6^2\\times D_4).C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 4], [6, 16], [12, 16], [24, 6]], 'representations': {'PC': {'code': 26483637328640604887636753813195914625454651697085, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -2, -2, -7, -2, -2, -7, 5488, 555, 58, 682, 52924, 12751, 102, 61157, 30588, 124, 65862, 32941]}, 'Perm': {'d': 24, 'gens': [26064415595284790635566, 25968823152520864958767, 1, 859975, 1275486, 55344551597557255756800, 82376623366764094368000]}}, 'schur_multiplier': [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.D_{14}^2', 'transitive_degree': 112, 'wreath_data': None, 'wreath_product': False}
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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}
