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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '192.837', 'ambient_counter': 837, 'ambient_order': 192, 'ambient_tex': 'C_{12}\\times \\OD_{16}', 'central': False, 'central_factor': False, 'centralizer_order': 96, 'characteristic': True, 'core_order': 96, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '192.837.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '2.a1', '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': False, 'standard_generators': False, 'stem': False, 'subgroup': '96.161', 'subgroup_hash': 161, 'subgroup_order': 96, 'subgroup_tex': 'C_2\\times C_4\\times C_{12}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '192.837', 'aut_centralizer_order': 8, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '256.29598', 'aut_weyl_index': 8, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '6.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [3986, 3338, 5918, 3655], 'generators': [1, 96, 4, 2, 48, 64], 'label': '192.837.2.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.a1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.a1', '4.b1', '4.c1', '4.d1', '4.e1', '6.a1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '4.2', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '2.1'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '96.161', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 2, 2, 6, 2, 2, 2, 4, 2], 'aut_gens': [[1, 2, 8], [49, 54, 56], [1, 50, 8], [1, 2, 40], [1, 75, 34], [1, 54, 8], [1, 54, 60], [1, 50, 56], [1, 26, 40], [53, 50, 12]], 'aut_group': '3072.bjj', 'aut_hash': 3278739220350440602, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 26, 'aut_perms': [156599506467661408882560, 156290489358596340678150, 1, 267810879463645168873558446, 156598898240815284791046, 2508820767086692523195520, 49067179719652537489161384, 15618248412000798990155431, 49067179719799053264666840], 'aut_phi_ratio': 96.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1], [2, 1, 4, 1], [3, 1, 2, 1], [4, 1, 24, 1], [6, 1, 6, 1], [6, 1, 8, 1], [12, 1, 48, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^7:S_4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 24, 'autcent_group': '3072.bjj', 'autcent_hash': 3278739220350440602, 'autcent_nilpotent': False, 'autcent_order': 3072, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': False, 'autcent_tex': 'C_2^7:S_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, 7], [3, 1, 2], [4, 1, 24], [6, 1, 14], [12, 1, 48]], 'center_label': '96.161', 'center_order': 96, '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', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 161, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 1, 2, 1], [4, 1, 2, 12], [6, 1, 2, 7], [12, 1, 4, 12]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 91, 'exponent': 12, 'exponents_of_order': [5, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '24.15', 'hash': 161, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1, 1], 'inner_gens': [[1, 2, 8], [1, 2, 8], [1, 2, 8]], '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, 96]], 'label': '96.161', 'linC_count': 46592, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 6, 'linQ_degree_count': 192, 'linQ_dim': 6, 'linQ_dim_count': 192, 'linR_count': 1536, 'linR_degree': 5, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C2*C4*C12', 'ngens': 6, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 8, 'number_characteristic_subgroups': 8, 'number_conjugacy_classes': 96, 'number_divisions': 40, 'number_normal_subgroups': 108, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 108, 'number_subgroups': 108, 'old_label': None, 'order': 96, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [6, 14], [12, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 24, 'outer_gen_orders': [2, 2, 2, 6, 2, 2, 2, 4, 2], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[49, 54, 56], [1, 50, 8], [1, 2, 40], [1, 75, 34], [1, 54, 8], [1, 54, 60], [1, 50, 56], [1, 26, 40], [53, 50, 12]], 'outer_group': '3072.bjj', 'outer_hash': 3278739220350440602, 'outer_nilpotent': False, 'outer_order': 3072, 'outer_permdeg': 26, 'outer_perms': [156599506467661408882560, 156290489358596340678150, 1, 267810879463645168873558446, 156598898240815284791046, 2508820767086692523195520, 49067179719652537489161384, 15618248412000798990155431, 49067179719799053264666840], 'outer_solvable': True, 'outer_supersolvable': False, 'outer_tex': 'C_2^7:S_4', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 13, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 12]], 'representations': {'PC': {'code': 638607951489, 'gens': [1, 2, 4], 'pres': [6, -2, -2, -2, -2, -2, -3, 31, 69, 88]}, 'GLZ': {'b': 3, 'd': 6, 'gens': [91655872443238928, 125101750005088212, 58438776791332585]}, 'GLFp': {'d': 3, 'p': 13, 'gens': [10319436418, 9789111396, 6526074264, 6878714910, 4548416880, 6762482606]}, 'Perm': {'d': 13, 'gens': [11612160, 2400, 479001600, 4, 3669120, 744]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 12], 'solvability_type': 2, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_4\\times C_{12}', 'transitive_degree': 96, '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': '96.161', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 2, 2, 4, 2, 4, 2, 4, 2, 2], 'aut_gens': [[1, 2, 8], [1, 102, 44], [97, 6, 184], [5, 98, 184], [1, 2, 108], [1, 6, 59], [1, 2, 92], [1, 102, 190], [1, 2, 104], [97, 146, 108], [1, 98, 104], [97, 98, 8]], 'aut_group': '2048.cru', 'aut_hash': 4755381471134919770, 'aut_nilpotency_class': 3, 'aut_nilpotent': True, 'aut_order': 2048, 'aut_permdeg': 34, 'aut_perms': [542707351178976785010150236982760080, 229666509439723429296776110743901596075, 229682945665896518402030829135104281633, 278680499871120120219403604589250083754, 142185482993057103150773034070606682819, 228211733151882771597714287979066925500, 204603693390420236148280397125478652240, 109902356355091904838041094531401514843, 53017700740344935329583827965879380322, 5702539871469389482739622967430652240, 173074785813402152592134449723732155], 'aut_phi_ratio': 32.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 2, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [4, 1, 8, 1], [4, 2, 2, 1], [4, 2, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [6, 2, 4, 1], [8, 2, 16, 1], [12, 1, 8, 1], [12, 1, 16, 1], [12, 2, 4, 1], [12, 2, 8, 1], [24, 2, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2^5.C_2^6', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '1024.dlb', 'autcent_hash': 7684842177144052536, 'autcent_nilpotent': True, 'autcent_order': 1024, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^7:D_4', 'autcentquo_abelian': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 2, 2], [3, 1, 2], [4, 1, 12], [4, 2, 6], [6, 1, 6], [6, 2, 4], [8, 2, 16], [12, 1, 24], [12, 2, 12], [24, 2, 32]], 'center_label': '48.20', 'center_order': 48, 'central_product': True, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', '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'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 837, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['16.6', 1], ['3.1', 1], ['4.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 2, 1, 2], [3, 1, 2, 1], [4, 1, 2, 6], [4, 2, 1, 2], [4, 2, 2, 2], [6, 1, 2, 3], [6, 2, 2, 2], [8, 2, 2, 8], [12, 1, 4, 6], [12, 2, 2, 2], [12, 2, 4, 2], [24, 2, 4, 8]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1092, 'exponent': 24, 'exponents_of_order': [6, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.2', 'frattini_quotient': '24.15', 'hash': 837, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 1, 2], 'inner_gens': [[1, 2, 104], [1, 2, 8], [97, 2, 8]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': False, 'inner_tex': 'C_2^2', 'inner_used': [1, 3], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 96], [2, 24]], 'label': '192.837', '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': 'C12*OD16', 'ngens': 7, 'nilpotency_class': 2, 'nilpotent': True, 'normal_counts': [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': 18, 'number_characteristic_subgroups': 22, 'number_conjugacy_classes': 120, 'number_divisions': 48, 'number_normal_subgroups': 122, 'number_subgroup_autclasses': 62, 'number_subgroup_classes': 142, 'number_subgroups': 162, 'old_label': None, 'order': 192, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 24], [6, 14], [8, 32], [12, 48], [24, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [2, 4, 2, 4, 2, 4], 'outer_gen_pows': [1, 0, 1, 0, 0, 0], 'outer_gens': [[1, 2, 91], [5, 146, 106], [97, 50, 188], [1, 146, 91], [97, 150, 89], [101, 150, 159]], 'outer_group': '512.7536352', 'outer_hash': 227827361366586539, 'outer_nilpotent': True, 'outer_order': 512, 'outer_permdeg': 128, 'outer_perms': [212222189969418459350044627701480312351379894902241204638032957799143927790322520507535015580246039620076835574741775618485717267723960411576404273557470914687348719648984147109615051749032890286266236399174922772676, 303111109803936989994175015210079018017776813875955383019182173447264484302387121419135425339216430162855471335671443873559230441585671003292194900910859247759690864679545095820687042025049146415280911242047524052900, 231448483022080498780830281624928823240009230306964989183452610454875893207733924891352154676122619338075509509388929375745212206592128281928967631041824701929379459902581590222810334053456223454442179634472373190030, 139215278277032662307655858837816890714782021171934578693125324712101899595838432942139802715496091338111994842676294069391269273514816615639238755635870874384622907409334638819220088572401208417037013687381574553836, 288880422654887204826822117036448680566454144620858807701057758058780989173223970243020127133228280806837249439369320429442476259033475975921231375415994268338189544788121873186782415062455913092135919375229115748527, 239575882380539783113072742450811187253836713645113364142441931581862223277619644964601238610248551776616398981512576456343468523539457883085257824515317823168185427719300637408003663976450451080630593105195405191603], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3.C_2^6', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 4, 3], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 20], [4, 16], [8, 4]], 'representations': {'PC': {'code': 93510159222712605953, 'gens': [1, 2, 4], 'pres': [7, -2, -2, -2, -2, -2, -2, -3, 36, 2915, 80, 102, 124]}, 'GLFp': {'d': 3, 'p': 13, 'gens': [478687413, 7172158309, 7395667683, 6411482571, 9789111396, 6526074264, 9095639691]}, 'Perm': {'d': 15, 'gens': [101239891944, 200705704104, 31658376960, 4, 298980460800, 381365833704, 381365832960]}}, 'schur_multiplier': [2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 4, 12], 'solvability_type': 4, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}\\times \\OD_{16}', 'transitive_degree': 96, '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}
