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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4400.m', 'ambient_counter': 13, 'ambient_order': 4400, 'ambient_tex': 'C_{44}.C_{10}^2', 'central': False, 'central_factor': False, 'centralizer_order': 20, 'characteristic': False, 'core_order': 2200, 'counter': 2, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '4400.m.2.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': None, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, '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': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '2200.b', 'subgroup_hash': 8674610327534484139, 'subgroup_order': 2200, 'subgroup_tex': 'C_{20}\\times F_{11}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4400.m', 'aut_centralizer_order': 4, 'aut_label': '2.a1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 12, 'centralizer': '220.a1', 'complements': [], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.a1', '4.b1', '4.c1', '10.a1', '10.b1', '22.a1'], 'core': '2.a1', 'coset_action_label': None, 'count': 3, 'diagramx': [4929, 4718, 4200, 3875], 'generators': [10, 400, 4, 880, 1100, 2200], 'label': '4400.m.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', '10.a1', '10.b1'], 'normalizer': '1.a1', 'old_label': '2.a1', 'projective_image': '440.42', 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '2.a1', 'subgroup_fusion': None, 'weyl_group': '220.7'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '200.37', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 220, 'aut_gen_orders': [44, 10, 4, 20, 20], 'aut_gens': [[1, 10], [401, 670], [241, 790], [661, 1970], [1101, 830], [281, 1070]], 'aut_group': None, 'aut_hash': 3452933427242197936, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 8800, 'aut_permdeg': 79, 'aut_perms': [76266791097571405496118289035625057462014978753798815006202172702224514744837042264982358209596789113209313572599700, 540636973929703130149179825559720911186370577939692833762576006822419544807276254431592478510438899647327823472412169, 223878176561419005465914929740852042774882254353572305033501331782355625882585546513030177684666278495464712064830598, 673766993856946267582253841065915668158769525860321996197390067955940058577604924386175482573491091825487705955923992, 425105849778774866809327770038184341739662106368223146098968965948895155158293727358469128109083002634331878997741468], 'aut_phi_ratio': 11.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [4, 1, 2, 1], [4, 11, 2, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 4, 1], [10, 11, 5, 4], [10, 11, 8, 1], [10, 11, 10, 4], [11, 10, 1, 1], [20, 1, 8, 1], [20, 11, 8, 1], [20, 11, 10, 8], [22, 10, 1, 1], [44, 10, 2, 1], [55, 10, 4, 1], [110, 10, 4, 1], [220, 10, 8, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{55}.C_{10}.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '80.50', 'autcent_hash': 50, 'autcent_nilpotent': False, 'autcent_order': 80, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 110, 'autcentquo_group': '110.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': False, 'autcentquo_order': 110, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [4, 1, 2], [4, 11, 2], [5, 1, 4], [5, 11, 20], [10, 1, 4], [10, 11, 68], [11, 10, 1], [20, 1, 8], [20, 11, 88], [22, 10, 1], [44, 10, 2], [55, 10, 4], [110, 10, 4], [220, 10, 8]], 'center_label': '20.2', 'center_order': 20, 'central_product': True, 'central_quotient': '110.1', 'commutator_count': 1, 'commutator_label': '11.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '5.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['110.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [4, 1, 2, 1], [4, 11, 2, 1], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 1], [10, 11, 4, 17], [11, 10, 1, 1], [20, 1, 8, 1], [20, 11, 8, 11], [22, 10, 1, 1], [44, 10, 2, 1], [55, 10, 4, 1], [110, 10, 4, 1], [220, 10, 8, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 220, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 0, 8]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '1100.29', 'hash': 8674610327534484139, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 11], 'inner_gens': [[1, 1010], [1201, 10]], 'inner_hash': 1, 'inner_nilpotent': False, 'inner_order': 110, 'inner_split': True, 'inner_tex': 'F_{11}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 20, 'irrep_stats': [[1, 200], [10, 20]], 'label': '2200.b', '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': 'C20*F11', 'ngens': 6, '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': 36, 'number_characteristic_subgroups': 24, 'number_conjugacy_classes': 220, 'number_divisions': 48, 'number_normal_subgroups': 70, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 128, 'number_subgroups': 708, 'old_label': None, 'order': 2200, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 23], [4, 24], [5, 224], [10, 752], [11, 10], [20, 976], [22, 10], [44, 20], [55, 40], [110, 40], [220, 80]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 4, 10], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1101, 210], [441, 1530], [1321, 1310]], 'outer_group': '80.50', 'outer_hash': 50, 'outer_nilpotent': False, 'outer_order': 80, 'outer_permdeg': 9, 'outer_perms': [7, 5887, 122536], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^2\\times F_5', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 5, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 2], [4, 24], [8, 12], [10, 2], [20, 1], [40, 2], [80, 1]], 'representations': {'PC': {'code': '40468999109068535014526304591694260475653013471030039', 'gens': [1, 3], 'pres': [6, -2, -5, -2, -2, -5, -11, 12, 6607, 18182, 7298, 50, 48483, 19449, 69, 55204, 15610, 178, 14405, 14411]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 28624986026014313, 33418192856010432, 38155586759637906, 11212492713789353, 23726635956891084]}, 'Perm': {'d': 20, 'gens': [51960, 6423384711840487, 131167, 13560777195488777, 140856425323943160, 51982]}}, 'schur_multiplier': [10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10, 20], 'solvability_type': 6, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{20}\\times F_{11}', 'transitive_degree': 220, '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': '200.52', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [10, 60, 12, 20, 20], 'aut_gens': [[1, 2, 20], [4316, 3122, 2685], [4396, 2602, 3105], [196, 2722, 1825], [2421, 642, 420], [1241, 3522, 2825]], 'aut_group': None, 'aut_hash': 333570381098051054, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 105600, 'aut_permdeg': 83, 'aut_perms': [1555750564830194189365818167316049118515730820254172870430299209378207112214587798433352009503664159661588417888550266258535, 30925874656572050026632831560543697614536016798283942523179543606857669881882668975401193508990631331796641210710672180435612, 16016153995587373590234130532119699956256783529628351478298656723848150907274674305151549848114365394944983733702028537211995, 35250534075927931843308016573561266339361049966756948979592167107945321095774225314123686903477870341728651171110467231148838, 18526419365673994712313357694661675149996324968304186846271297412930531710982138630026035546497560961994497085219536489711342], 'aut_phi_ratio': 66.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 2, 1], [4, 2, 3, 1], [4, 22, 3, 1], [5, 1, 4, 1], [5, 11, 5, 4], [10, 1, 4, 1], [10, 11, 5, 4], [10, 11, 8, 1], [10, 11, 10, 4], [11, 10, 1, 1], [20, 2, 12, 1], [20, 22, 12, 1], [20, 22, 15, 8], [22, 10, 1, 1], [44, 20, 3, 1], [55, 10, 4, 1], [110, 10, 4, 1], [220, 20, 12, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2.C_{165}.C_{10}.C_2^4', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '160.236', 'autcent_hash': 236, 'autcent_nilpotent': False, 'autcent_order': 160, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^3\\times F_5', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '660.15', 'autcentquo_hash': 15, 'autcentquo_nilpotent': False, 'autcentquo_order': 660, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'S_3\\times F_{11}', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 11, 2], [4, 2, 3], [4, 22, 3], [5, 1, 4], [5, 11, 20], [10, 1, 4], [10, 11, 68], [11, 10, 1], [20, 2, 12], [20, 22, 132], [22, 10, 1], [44, 20, 3], [55, 10, 4], [110, 10, 4], [220, 20, 12]], 'center_label': '10.2', 'center_order': 10, 'central_product': True, 'central_quotient': '440.42', 'commutator_count': 1, 'commutator_label': '22.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '5.1', '5.1', '11.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 13, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['110.1', 1], ['5.1', 1], ['8.4', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 11, 1, 2], [4, 2, 1, 3], [4, 22, 1, 3], [5, 1, 4, 1], [5, 11, 4, 5], [10, 1, 4, 1], [10, 11, 4, 17], [11, 10, 1, 1], [20, 2, 4, 3], [20, 22, 4, 33], [22, 10, 1, 1], [44, 20, 1, 3], [55, 10, 4, 1], [110, 10, 4, 1], [220, 20, 4, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 249984, 'exponent': 220, 'exponents_of_order': [4, 2, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[20, 0, 4]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '2200.a', 'hash': 7359625474499212845, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [10, 10, 22], 'inner_gens': [[1, 2002, 1820], [2401, 2, 2020], [2601, 2402, 20]], 'inner_hash': 42, 'inner_nilpotent': False, 'inner_order': 440, 'inner_split': True, 'inner_tex': 'C_2^2\\times F_{11}', 'inner_used': [1, 2, 3], 'irrC_degree': 20, 'irrQ_degree': 80, 'irrQ_dim': 80, 'irrR_degree': 40, 'irrep_stats': [[1, 200], [2, 50], [10, 20], [20, 5]], 'label': '4400.m', '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': 'C44.C10^2', '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, 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': 36, 'number_characteristic_subgroups': 21, 'number_conjugacy_classes': 275, 'number_divisions': 80, 'number_normal_subgroups': 164, 'number_subgroup_autclasses': 80, 'number_subgroup_classes': 304, 'number_subgroups': 1704, 'old_label': None, 'order': 4400, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 23], [4, 72], [5, 224], [10, 752], [11, 10], [20, 2928], [22, 10], [44, 60], [55, 40], [110, 40], [220, 240]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 60, 'outer_gen_orders': [2, 4, 30], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[1356, 2, 285], [876, 882, 2525], [476, 442, 3585]], 'outer_group': '240.195', 'outer_hash': 195, 'outer_nilpotent': False, 'outer_order': 240, 'outer_permdeg': 10, 'outer_perms': [7, 46087, 1099489], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'D_6\\times F_5', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 5, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 2], [4, 48], [8, 12], [10, 4], [20, 1], [40, 4], [80, 1]], 'representations': {'PC': {'code': '1539018528973074079978991569647978877460577145669761487615340476114120171470030039', 'gens': [1, 2, 4], 'pres': [7, -2, -2, -5, -2, -2, -5, -11, 27244, 28029, 36, 33686, 50963, 28290, 11357, 80, 127404, 70711, 28368, 102, 120965, 77292, 21859, 250, 58806, 19613, 19620]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 31318850038632571, 39096446745583924, 41217174402924011, 29417756511587215, 33418192856010432, 23726635956891084]}, 'Perm': {'d': 24, 'gens': [33, 29482547546685500467233, 4603563859131472435264, 486985713, 52013621325460976143264, 80933046670022808522960, 109189379508851625984090]}}, 'schur_multiplier': [2, 10], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 10, 10], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{44}.C_{10}^2', 'transitive_degree': 440, '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}
