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gps_subgroup_search • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '768.1090131', 'ambient_counter': 1090131, 'ambient_order': 768, 'ambient_tex': 'C_2^5:S_4', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 384, 'counter': 4, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '768.1090131.2.b1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1.b1', 'outer_equivalence': False, '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': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '384.18135', 'subgroup_hash': 18135, 'subgroup_order': 384, 'subgroup_tex': 'C_4^2:S_4', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '768.1090131', 'aut_centralizer_order': 1, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 2, 'aut_weyl_group': '3072.bgb', 'aut_weyl_index': 2, 'centralizer': '384.a1.a1', 'complements': ['384.f1.a1', '384.a1.a1', '384.b1.a1', '384.d1.a1', '384.d1.b1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.a1.a1', '6.h1.b1', '8.d1.b1', '8.d1.d1', '8.e1.b1'], 'core': '2.b1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [1464, 2258, 937, 902, 1397, 2802, 6340, 2827], 'generators': [84307934393430, 1822337812123926, 312321447414, 359890668365808, 461960891286, 1558054095215088, 3846242716609368, 85621839894847], 'label': '768.1090131.2.b1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.a1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.b1.b1', 'projective_image': '768.1090131', 'quotient_action_image': '2.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '2.b1.b1', 'subgroup_fusion': None, 'weyl_group': '384.18135'}
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gps_groups • Show schema
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{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '2.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [8, 4, 8], 'aut_gens': [[6210625, 5484311, 32746561, 5128257, 4572257, 10625677, 10024001, 32085027], [10625677, 7640717, 17779341, 6912475, 12133051, 32746561, 6558349, 5535779], [10752791, 20510487, 30362391, 11487707, 10733304, 8375361, 6431511, 29556216], [11487707, 12570075, 6912475, 17779341, 8327867, 19208257, 16916955, 11815598]], 'aut_group': '3072.bgb', 'aut_hash': 7983714371117797868, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 3072, 'aut_permdeg': 24, 'aut_perms': [213354243682994391041122, 497197691147596011620008, 527443102910431391045928], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 12, 2, 1], [2, 24, 1, 1], [3, 128, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 48, 2, 1], [8, 48, 1, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^3:(C_2\\times S_4)', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 24, 'autcentquo_group': '3072.bgb', 'autcentquo_hash': 7983714371117797868, 'autcentquo_nilpotent': False, 'autcentquo_order': 3072, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^3:(C_2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 3, 1], [2, 12, 2], [2, 24, 1], [3, 128, 1], [4, 12, 1], [4, 24, 2], [4, 48, 2], [8, 48, 1]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '384.18135', 'commutator_count': 1, 'commutator_label': '192.1023', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 18135, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 3, 1, 1], [2, 12, 1, 2], [2, 24, 1, 1], [3, 128, 1, 1], [4, 12, 1, 1], [4, 24, 1, 2], [4, 48, 1, 2], [8, 48, 1, 1]], 'element_repr_type': 'GLFp', 'elementary': 1, 'eulerian_function': 9, 'exponent': 24, 'exponents_of_order': [7, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '96.227', 'hash': 18135, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 4, 2, 2, 4, 2, 2, 3], 'inner_gens': [[6210625, 9805591, 32746561, 5128257, 5587041, 17779341, 10024001, 20914211], [10024001, 5484311, 20290625, 31664193, 33040481, 17779341, 6210625, 5837685], [6210625, 9805591, 32746561, 5128257, 20846689, 17779341, 10024001, 5535779], [6210625, 33474327, 32746561, 5128257, 5587041, 29981325, 10024001, 18753571], [5128257, 32391959, 8941633, 6210625, 4572257, 16916955, 31664193, 19133538], [32746561, 33474327, 6210625, 19208257, 4453879, 10625677, 20290625, 31641327], [6210625, 9805591, 32746561, 5128257, 20846689, 17779341, 10024001, 9586723], [8941633, 32010893, 5128257, 12188737, 19201058, 16916955, 31664193, 32085027]], 'inner_hash': 18135, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': True, 'inner_tex': 'C_4^2:S_4', 'inner_used': [1, 2, 3, 4, 5, 6, 8], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 2], [2, 1], [3, 6], [6, 1], [12, 2]], 'label': '384.18135', 'linC_count': 2, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C4^2:S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 12, 'number_divisions': 12, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 120, 'number_subgroups': 1200, 'old_label': None, 'order': 384, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 51], [3, 128], [4, 156], [8, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 4], 'outer_gen_pows': [17043521, 17043521], 'outer_gens': [[32746561, 33474327, 6210625, 8941633, 32025697, 10625677, 20290625, 4520995], [10625677, 7640717, 17779341, 29626843, 29556411, 32746561, 6558349, 32085027]], 'outer_group': '8.3', 'outer_hash': 3, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 4, 'outer_perms': [1, 17], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 16, 'pgroup': 0, 'primary_abelian_invariants': [2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 1], [3, 6], [6, 1], [12, 2]], 'representations': {'PC': {'code': 1991679335709088258385818832688287937798566951163646016, 'gens': [1, 2, 3, 4, 5, 7], 'pres': [8, 2, 3, 2, 2, 2, 2, 2, 2, 65, 434, 226, 107, 4804, 1932, 1460, 908, 116, 11525, 4621, 16134, 10094, 1366, 1374, 166, 7695]}, 'GLFp': {'d': 5, 'p': 2, 'gens': [6210625, 5484311, 32746561, 5128257, 4572257, 10625677, 10024001, 32085027]}, 'Perm': {'d': 16, 'gens': [6403179001, 174539660260, 4103606718727, 2789832689287, 11212821043200, 5606234750016, 2789792421136, 1313941673647]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_4^2:S_4', 'transitive_degree': 16, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 4, 'aut_exponent': 24, 'aut_gen_orders': [2, 4, 4, 4, 6], 'aut_gens': [[85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345214, 1, 1800200723874894, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345215, 1, 737186240310024, 1821883084207920, 795340005803406, 5621224034334630, 1558054095215088, 1822337812123926, 795533260057254], [2670559180032990, 1, 2730880140856584, 4088283555510366, 4466613169859766, 1822038947023848, 1821696294042054, 359890668365808, 795533260057254], [3353416120037551, 1, 3292827135187014, 795788474029920, 360096412929840, 4088283555510366, 3437629559701230, 359890668365808, 795533260057254], [4913965112744520, 1, 2353504295850726, 735925055088, 795203061792528, 3437629559701230, 4934975208295326, 795533260057254, 1822337812123926]], 'aut_group': '6144.ze', 'aut_hash': 4158378184127417885, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6144, 'aut_permdeg': 48, 'aut_perms': [9994073346956691326310842053270612521722600417121765690395696, 11053973361945428615465185065217005606706706163177450420395046, 3820124437949437479010256854732253317884941161210171750861093, 6009849731016979477797640346594027687778683254932669762820388, 1059547849389346313480217742049924904175648835892817432484552], 'aut_phi_ratio': 24.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 2, 2], [2, 24, 2, 1], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 2], [4, 24, 2, 1], [4, 48, 4, 1], [6, 128, 1, 1], [8, 48, 2, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_4^3:(C_2^2\\times S_4)', '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': '3072.bgb', 'autcentquo_hash': 7983714371117797868, 'autcentquo_nilpotent': False, 'autcentquo_order': 3072, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_4^3:(C_2\\times S_4)', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [2, 12, 4], [2, 24, 2], [3, 128, 1], [4, 12, 2], [4, 24, 4], [4, 48, 4], [6, 128, 1], [8, 48, 2]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '384.18135', 'commutator_count': 1, 'commutator_label': '192.1023', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '2.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 1090131, 'cyclic': False, 'derived_length': 4, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['384.18135', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [2, 12, 1, 4], [2, 24, 1, 2], [3, 128, 1, 1], [4, 12, 1, 2], [4, 24, 1, 4], [4, 48, 1, 4], [6, 128, 1, 1], [8, 48, 1, 2]], 'element_repr_type': 'Perm', 'elementary': 1, 'eulerian_function': 9, 'exponent': 24, 'exponents_of_order': [8, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[12, 1, 2]], 'familial': False, 'frattini_label': '4.2', 'frattini_quotient': '192.1538', 'hash': 1090131, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 24, 'inner_gen_orders': [2, 1, 3, 2, 2, 2, 2, 2, 2], 'inner_gens': [[85621839894847, 1, 84307934393430, 1821883084207920, 795340005803406, 3846242716609368, 1558054095215088, 1822337812123926, 795533260057254], [85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [21010095550807, 1, 25057722413880, 795340005803406, 1821883084207920, 1558054095215088, 3846242716609368, 795533260057254, 1822337812123926], [733176358717801, 1, 1799920432122126, 359728823398326, 795340005803406, 2208813870141024, 4466613169859766, 359890668365808, 795533260057254], [85621839894847, 1, 441265441118040, 359728823398326, 795340005803406, 4088283555510366, 3437629559701230, 359890668365808, 795533260057254], [1663625494874185, 1, 3865752002090880, 312321447414, 360096412929840, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 1226009285991720, 795788474029920, 735925055088, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [733382477345215, 1, 1800200723874894, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 441097551912486, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254]], 'inner_hash': 18135, 'inner_nilpotent': False, 'inner_order': 384, 'inner_split': True, 'inner_tex': 'C_4^2:S_4', 'inner_used': [1, 3, 4, 6], 'irrC_degree': 12, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 4], [2, 2], [3, 12], [6, 2], [12, 4]], 'label': '768.1090131', 'linC_count': 2, 'linC_degree': 12, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 12, 'linQ_degree_count': 2, 'linQ_dim': 12, 'linQ_dim_count': 2, 'linR_count': 2, 'linR_degree': 12, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2^5:S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 16, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 24, 'number_divisions': 24, 'number_normal_subgroups': 17, 'number_subgroup_autclasses': 273, 'number_subgroup_classes': 528, 'number_subgroups': 5446, 'old_label': None, 'order': 768, 'order_factorization_type': 51, 'order_stats': [[1, 1], [2, 103], [3, 128], [4, 312], [6, 128], [8, 96]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 2, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[85621839894846, 1, 25057722413880, 312321447414, 735925055088, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254], [85621839894847, 1, 25057722413880, 2208813870141024, 3437629559701230, 312321447414, 735925055088, 359890668365808, 795533260057254], [85621839894846, 1, 25057722413880, 312321447414, 735925055088, 2208813870141024, 3437629559701230, 359890668365808, 795533260057254], [85621839894847, 1, 25057722413880, 312321447414, 735925055088, 2208813870141024, 3437629559701230, 359890668365808, 795533260057254]], 'outer_group': '16.11', 'outer_hash': 11, 'outer_nilpotent': True, 'outer_order': 16, 'outer_permdeg': 6, 'outer_perms': [6, 289, 127, 126], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_4', 'pc_rank': 6, 'perfect': False, 'permutation_degree': 18, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [3, 12], [6, 2], [12, 4]], 'representations': {'PC': {'code': '79924844233235786991899159435981848360229194954850928243109730413695879780301013992512', 'gens': [1, 2, 4, 5, 6, 8], 'pres': [9, 2, 2, 3, 2, 2, 2, 2, 2, 2, 181, 46, 218, 1299, 444, 345, 823, 157, 36941, 18158, 3263, 1976, 365, 158, 30246, 12111, 7584, 12967, 12112, 7801, 1762, 2059, 214, 19457, 1970]}, 'Perm': {'d': 18, 'gens': [85621839894847, 1, 25057722413880, 359728823398326, 795340005803406, 1179562541714328, 1558054095215088, 359890668365808, 795533260057254]}}, 'schur_multiplier': [2, 2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2^5:S_4', 'transitive_degree': 24, '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}
