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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '1728.47311', 'ambient_counter': 47311, 'ambient_order': 1728, 'ambient_tex': 'C_{12}.D_6^2', 'central': False, 'central_factor': False, 'centralizer_order': 8, 'characteristic': True, 'core_order': 432, 'counter': 31, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1728.47311.4.o1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '4.o1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '4.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': False, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 4, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_2^2', 'simple': False, 'solvable': True, 'special_labels': [], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '432.721', 'subgroup_hash': 721, 'subgroup_order': 432, 'subgroup_tex': 'C_6^2.D_6', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '1728.47311', 'aut_centralizer_order': None, 'aut_label': '4.o1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '216.a1', 'complements': [], 'conjugacy_class_count': 1, 'contained_in': ['2.d1', '2.i1', '2.k1'], 'contains': ['8.d1', '8.e1', '8.k1', '8.z1', '12.cg1', '12.ci1', '12.ck1', '12.cl1', '12.cn1', '12.co1', '12.cq1'], 'core': '4.o1', 'coset_action_label': None, 'count': 1, 'diagramx': None, 'generators': [147, 96, 16, 12, 576, 864, 24], 'label': '1728.47311.4.o1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '4.o1', 'normal_contained_in': ['2.d1', '2.i1', '2.k1'], 'normal_contains': ['8.d1', '8.e1', '8.k1', '8.z1'], 'normalizer': '1.a1', 'old_label': '4.o1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '4.o1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, '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': 936, 'aut_gen_orders': [12, 26, 36, 18, 24], 'aut_gens': [[1, 2, 6, 36], [77, 2, 294, 428], [171, 302, 20, 202], [29, 312, 80, 418], [383, 160, 320, 426], [301, 290, 8, 56]], 'aut_group': None, 'aut_hash': 7192182936669174149, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 9704448, 'aut_permdeg': 112, 'aut_perms': [175419450305754997212326771840393897139555157044269875096830644756129340987150591234541587857875005482472223481929301431597407467025259293904237597872292604858846235402068347438485782, 13834579049422799258314997804762305950047455114010801526658673512443272095731803981898745646048027151014030580234680644799469548394951584018118478637470371701562387403793592205595651, 131351194026413279462938460516461182159553240736560499109173687261470103058517082389652531370307791840607892423133106537774583265589262924211811899520315314854233299688265036195631986, 27422637112661942261422853409206588201764551757056886275917134459993579108840134194053675527820843513236965340144494162656431681821685845410458642681216105819167466916393952872831945, 32650438307430297564914160860205326919623637400994867220731843917470783251310571051504956398059247198823906513099446900884571030496980237739103494251253565703399315340639549682468501], 'aut_phi_ratio': 67392.0, 'aut_solvable': False, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 27, 4, 1], [3, 2, 13, 1], [4, 1, 4, 1], [4, 27, 4, 1], [6, 2, 13, 1], [6, 2, 26, 1], [12, 2, 52, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_6^3.C_2^3.\\SL(3,3)', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '32.27', 'autcent_hash': 27, 'autcent_nilpotent': True, 'autcent_order': 32, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2\\wr C_2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 936, 'autcentquo_group': '303264.a', 'autcentquo_hash': 8091482650397092313, 'autcentquo_nilpotent': False, 'autcentquo_order': 303264, 'autcentquo_solvable': False, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_3^3:\\GL(3,3)', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 27, 4], [3, 2, 13], [4, 1, 4], [4, 27, 4], [6, 2, 39], [12, 2, 52]], 'center_label': '8.2', 'center_order': 8, 'central_product': True, 'central_quotient': '54.14', 'commutator_count': 1, 'commutator_label': '27.5', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 721, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['4.1', 1], ['54.14', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 27, 1, 4], [3, 2, 1, 13], [4, 1, 2, 2], [4, 27, 2, 2], [6, 2, 1, 39], [12, 2, 2, 26]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 1260, 'exponent': 12, 'exponents_of_order': [4, 3], 'factors_of_aut_order': [2, 3, 13], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '216.176', 'hash': 721, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 3, 3, 3], 'inner_gens': [[1, 4, 30, 180], [5, 2, 6, 36], [13, 2, 6, 36], [289, 2, 6, 36]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 54, 'inner_split': True, 'inner_tex': 'C_3^2:S_3', 'inner_used': [1, 2, 3, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 104]], 'label': '432.721', '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': 'C6^2.D6', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 10, 'number_characteristic_subgroups': 11, 'number_conjugacy_classes': 120, 'number_divisions': 90, 'number_normal_subgroups': 243, 'number_subgroup_autclasses': 56, 'number_subgroup_classes': 756, 'number_subgroups': 3720, 'old_label': None, 'order': 432, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 111], [3, 26], [4, 112], [6, 78], [12, 104]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 312, 'outer_gen_orders': [8, 12, 26, 2], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[235, 288, 236, 66], [235, 168, 82, 44], [1, 146, 162, 142], [19, 156, 152, 46]], 'outer_group': None, 'outer_hash': 9042163827247810672, 'outer_nilpotent': False, 'outer_order': 179712, 'outer_permdeg': 21, 'outer_perms': [28032844720139453969, 24336870139700266769, 7933701191533292133, 10718286716188011967], 'outer_solvable': False, 'outer_supersolvable': False, 'outer_tex': 'C_2^2\\wr C_2.\\SL(3,3)', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 56], [4, 26]], 'representations': {'PC': {'code': 20936216025170396826197608102441, 'gens': [1, 2, 3, 5], 'pres': [7, -2, -3, -2, -3, -2, -2, -3, 57, 632, 58, 675, 6304, 102, 15125, 124, 14118]}, 'GLZN': {'d': 2, 'p': 30, 'gens': [189007, 386866, 40966, 297011, 513019, 32773, 27301]}, 'Perm': {'d': 15, 'gens': [6266978047, 39916800, 17, 7, 93405312000, 93405716040, 404640]}}, 'schur_multiplier': [6, 6, 6], '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_6^2.D_6', 'transitive_degree': 216, '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': '32.51', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': None, 'aut_cyclic': None, 'aut_derived_length': None, 'aut_exponent': None, 'aut_gen_orders': None, 'aut_gens': [[1, 2, 4, 48, 288], [25, 2, 4, 48, 1440], [1, 26, 4, 240, 1440], [1, 2, 44, 48, 1440], [1, 2, 4, 72, 1440], [1, 2, 20, 240, 312], [13, 14, 4, 240, 288], [1, 2, 4, 1104, 288], [1, 2, 868, 912, 288], [1, 866, 868, 1104, 288], [1, 2, 20, 48, 288], [1, 2, 4, 240, 288], [1, 2, 4, 48, 1440], [17, 2, 4, 48, 288], [1, 98, 4, 48, 288], [1, 2, 4, 624, 288]], 'aut_group': '2916.kq', 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 221184, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 6, 4, 1], [2, 18, 2, 1], [2, 54, 2, 1], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 2, 1], [4, 6, 2, 1], [4, 6, 4, 1], [4, 18, 2, 1], [4, 18, 4, 2], [4, 54, 2, 1], [6, 2, 1, 3], [6, 2, 2, 3], [6, 4, 1, 3], [6, 4, 2, 3], [6, 6, 4, 1], [6, 8, 1, 1], [6, 8, 2, 1], [6, 12, 2, 1], [6, 12, 4, 3], [6, 24, 4, 1], [6, 36, 2, 1], [12, 4, 2, 3], [12, 4, 4, 1], [12, 6, 4, 1], [12, 8, 2, 2], [12, 8, 4, 1], [12, 12, 2, 1], [12, 12, 4, 3], [12, 18, 4, 1], [12, 24, 4, 1], [12, 36, 4, 2]], 'aut_supersolvable': None, 'aut_tex': 'C_3^4:C_6^2', 'autcent_abelian': None, 'autcent_cyclic': None, 'autcent_exponent': None, 'autcent_group': None, 'autcent_hash': None, 'autcent_nilpotent': None, 'autcent_order': None, 'autcent_solvable': None, 'autcent_split': None, 'autcent_supersolvable': None, 'autcent_tex': None, 'autcentquo_abelian': None, 'autcentquo_cyclic': None, 'autcentquo_exponent': None, 'autcentquo_group': None, 'autcentquo_hash': None, 'autcentquo_nilpotent': None, 'autcentquo_order': None, 'autcentquo_solvable': None, 'autcentquo_supersolvable': None, 'autcentquo_tex': None, 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 6], [2, 18, 2], [2, 54, 2], [3, 2, 3], [3, 4, 3], [3, 8, 1], [4, 2, 2], [4, 6, 6], [4, 18, 10], [4, 54, 2], [6, 2, 9], [6, 4, 9], [6, 6, 4], [6, 8, 3], [6, 12, 14], [6, 24, 4], [6, 36, 2], [12, 4, 10], [12, 6, 4], [12, 8, 8], [12, 12, 14], [12, 18, 4], [12, 24, 4], [12, 36, 8]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '432.759', 'commutator_count': 1, 'commutator_label': '54.15', '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', '3.1', '3.1'], 'composition_length': 9, 'conjugacy_classes_known': True, 'counter': 47311, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['864.4360', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 6], [2, 18, 1, 2], [2, 54, 1, 2], [3, 2, 1, 3], [3, 4, 1, 3], [3, 8, 1, 1], [4, 2, 1, 2], [4, 6, 1, 6], [4, 18, 1, 10], [4, 54, 1, 2], [6, 2, 1, 9], [6, 4, 1, 9], [6, 6, 2, 2], [6, 8, 1, 3], [6, 12, 1, 10], [6, 12, 2, 2], [6, 24, 1, 4], [6, 36, 1, 2], [12, 4, 1, 6], [12, 4, 2, 2], [12, 6, 2, 2], [12, 8, 1, 4], [12, 8, 2, 2], [12, 12, 1, 10], [12, 12, 2, 2], [12, 18, 2, 2], [12, 24, 1, 4], [12, 36, 1, 8]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 19998720000, 'exponent': 12, 'exponents_of_order': [6, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '864.4704', 'hash': 47311, 'hyperelementary': 1, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 432, 'inner_split': None, 'inner_tex': 'C_2\\times S_3^3', 'inner_used': None, 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 32], [2, 48], [4, 46], [8, 12]], 'label': '1728.47311', '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.D6^2', '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, 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': 58, 'number_characteristic_subgroups': 80, 'number_conjugacy_classes': 138, 'number_divisions': 124, 'number_normal_subgroups': 652, 'number_subgroup_autclasses': 1056, 'number_subgroup_classes': 3714, 'number_subgroups': 24884, 'old_label': None, 'order': 1728, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 183], [3, 26], [4, 328], [6, 438], [12, 752]], 'outer_abelian': None, 'outer_cyclic': None, 'outer_equivalence': True, 'outer_exponent': None, 'outer_gen_orders': None, 'outer_gen_pows': None, 'outer_gens': None, 'outer_group': '512.519620', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 512, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_2^6:D_4', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 27, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2, 2], 'quasisimple': False, 'rank': 5, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 32], [2, 48], [4, 26], [8, 14], [16, 4]], 'representations': {'PC': {'code': 6391722000760265967437605425818296741826302978840943125, 'gens': [1, 2, 3, 6, 8], 'pres': [9, 2, 2, 2, 2, 3, 2, 3, 2, 3, 216, 1190, 389, 74, 1443, 102, 1444, 7142, 158, 6063, 2212, 214, 1997]}, 'Perm': {'d': 27, 'gens': [405880137023713854056755920, 886834641045759912182839680, 1306778286713649760857369601, 24, 1617641616052166198181811200, 2083699538098702282317081600, 3991680, 5760, 3]}}, 'schur_multiplier': [2, 2, 2, 2, 2, 2, 2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 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_{12}.D_6^2', 'transitive_degree': 96, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 6, 'aut_gen_orders': [2, 3], 'aut_gens': [[1, 2], [3, 2], [2, 3]], 'aut_group': '6.1', 'aut_hash': 1, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 6, 'aut_permdeg': 3, 'aut_perms': [1, 4], 'aut_phi_ratio': 3.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 3, 1]], 'aut_supersolvable': True, 'aut_tex': 'S_3', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 6, 'autcent_group': '6.1', 'autcent_hash': 1, 'autcent_nilpotent': False, 'autcent_order': 6, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'S_3', '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, 3]], 'center_label': '4.2', 'center_order': 4, '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'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': False, 'derived_length': 1, 'dihedral': True, 'direct_factorization': [['2.1', 2]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 1, 'exponent': 2, 'exponents_of_order': [2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2], 'faithful_reps': [], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '4.2', 'hash': 2, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': True, 'inner_exponent': 1, 'inner_gen_orders': [1, 1], 'inner_gens': [[1, 2], [1, 2]], '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, 4]], 'label': '4.2', 'linC_count': 3, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 3, 'linQ_dim': 2, 'linQ_dim_count': 3, 'linR_count': 3, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2^2', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 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': 4, 'number_divisions': 4, 'number_normal_subgroups': 5, 'number_subgroup_autclasses': 3, 'number_subgroup_classes': 5, 'number_subgroups': 5, 'old_label': None, 'order': 4, 'order_factorization_type': 2, 'order_stats': [[1, 1], [2, 3]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 3], 'outer_gen_pows': [0, 0], 'outer_gens': [[3, 2], [2, 3]], 'outer_group': '6.1', 'outer_hash': 1, 'outer_nilpotent': False, 'outer_order': 6, 'outer_permdeg': 3, 'outer_perms': [1, 4], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'S_3', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 4, 'pgroup': 2, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': True, 'rational_characters_known': True, 'ratrep_stats': [[1, 4]], 'representations': {'PC': {'code': 0, 'gens': [1, 2], 'pres': [2, -2, 2]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 12]}, 'GLFp': {'d': 2, 'p': 3, 'gens': [55, 56]}, 'Perm': {'d': 4, 'gens': [6, 1]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2^2', 'transitive_degree': 4, 'wreath_data': None, 'wreath_product': False}
