-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '1344.11566', 'ambient_counter': 11566, 'ambient_order': 1344, 'ambient_tex': 'C_{84}.C_2^4', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': False, 'core_order': 672, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '1344.11566.2.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.b1', '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': True, 'standard_generators': False, 'stem': False, 'subgroup': '672.1134', 'subgroup_hash': 1134, 'subgroup_order': 672, 'subgroup_tex': 'D_{84}:C_2^2', 'supersolvable': True, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '1344.11566', 'aut_centralizer_order': 2, 'aut_label': '2.b1', 'aut_quo_index': 1, 'aut_stab_index': 3, 'aut_weyl_group': None, 'aut_weyl_index': 6, 'centralizer': '336.a1', 'complements': ['672.b1', '672.f1', '672.d1', '672.e1'], 'conjugacy_class_count': 3, 'contained_in': ['1.a1'], 'contains': ['4.b1', '4.c1', '4.j1', '4.k1', '4.l1', '4.t1', '4.u1', '4.y1', '4.z1', '6.c1', '14.c1'], 'core': '2.b1', 'coset_action_label': None, 'count': 3, 'diagramx': [3240, 5534, 3307, 4651], 'generators': [1, 448, 1316, 8, 2, 192, 16], 'label': '1344.11566.2.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.b1', 'normal_contained_in': ['1.a1'], 'normal_contains': ['4.b1', '4.c1', '4.j1', '4.k1', '4.l1', '4.t1', '4.u1', '4.y1', '4.z1'], 'normalizer': '1.a1', 'old_label': '2.b1', 'projective_image': '672.1271', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.b1', 'subgroup_fusion': None, 'weyl_group': '336.219'}
-
gps_groups • Show schema
Hide schema
{'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': 2, 'aut_exponent': 84, 'aut_gen_orders': [42, 12, 6, 6, 84, 6, 28], 'aut_gens': [[1, 2, 4, 8], [453, 646, 4, 12], [5, 218, 340, 520], [561, 206, 4, 184], [561, 322, 4, 636], [453, 574, 4, 8], [5, 102, 4, 488], [229, 250, 340, 572]], 'aut_group': None, 'aut_hash': 8662371451100837692, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 64512, 'aut_permdeg': 68, 'aut_perms': [1209043292346002888057385435775195914650767354522599631164532464888234342278774426422692674885859, 38087622548175834682262692306275625882306963437264698739312537999230864793248559814327051555409, 1204482555765696128166794155431550537140080119268925286243565826589056360209801800266128770417092, 2460620755159334691627983667031199399735528988061825065850240500639408518798669686696993547233617, 1533696629100995162078984905870737724357523827006375475713344504280875890737397696650541486556711, 216683325159667029663788436396041190029480056889797586576662056630578145369630951604225037559649, 1239964091310931303039797003545130378446919418495353450167068894042715226905349141649447023909525], 'aut_phi_ratio': 336.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [2, 6, 2, 1], [2, 42, 4, 1], [3, 2, 1, 1], [4, 2, 2, 1], [4, 3, 4, 1], [4, 14, 4, 1], [6, 2, 1, 1], [6, 2, 2, 1], [7, 2, 3, 1], [12, 4, 2, 1], [12, 28, 4, 1], [14, 2, 3, 1], [14, 2, 6, 1], [14, 6, 12, 1], [21, 4, 3, 1], [28, 2, 12, 1], [28, 6, 12, 1], [42, 4, 3, 1], [42, 4, 6, 1], [84, 4, 12, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_{42}.(C_2^5\\times C_6).C_2^3', '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': 42, 'autcentquo_group': '504.162', 'autcentquo_hash': 162, 'autcentquo_nilpotent': False, 'autcentquo_order': 504, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'D_6\\times F_7', 'cc_stats': [[1, 1, 1], [2, 1, 3], [2, 6, 2], [2, 42, 4], [3, 2, 1], [4, 2, 2], [4, 3, 4], [4, 14, 4], [6, 2, 3], [7, 2, 3], [12, 4, 2], [12, 28, 4], [14, 2, 9], [14, 6, 12], [21, 4, 3], [28, 2, 12], [28, 6, 12], [42, 4, 9], [84, 4, 12]], 'center_label': '4.2', 'center_order': 4, 'central_product': True, 'central_quotient': '168.50', 'commutator_count': 1, 'commutator_label': '42.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '7.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 1134, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['336.142', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 6, 1, 2], [2, 42, 1, 4], [3, 2, 1, 1], [4, 2, 1, 2], [4, 3, 2, 2], [4, 14, 1, 4], [6, 2, 1, 3], [7, 2, 3, 1], [12, 4, 1, 2], [12, 28, 1, 4], [14, 2, 3, 3], [14, 6, 6, 2], [21, 4, 3, 1], [28, 2, 6, 2], [28, 6, 6, 2], [42, 4, 3, 3], [84, 4, 6, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 933660, 'exponent': 84, 'exponents_of_order': [5, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '336.219', 'hash': 1134, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 42, 'inner_gen_orders': [2, 2, 1, 42], 'inner_gens': [[1, 2, 4, 232], [1, 2, 4, 664], [1, 2, 4, 8], [449, 18, 4, 8]], 'inner_hash': 50, 'inner_nilpotent': False, 'inner_order': 168, 'inner_split': False, 'inner_tex': 'S_3\\times D_{14}', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 16], [2, 60], [4, 26]], 'label': '672.1134', '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': 'D84:C2^2', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 23, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 102, 'number_divisions': 44, 'number_normal_subgroups': 116, 'number_subgroup_autclasses': 120, 'number_subgroup_classes': 328, 'number_subgroups': 2152, 'old_label': None, 'order': 672, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 183], [3, 2], [4, 72], [6, 6], [7, 6], [12, 120], [14, 90], [21, 12], [28, 96], [42, 36], [84, 48]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 12, 'outer_gen_orders': [2, 2, 4, 4, 6], 'outer_gen_pows': [0, 0, 0, 0, 0], 'outer_gens': [[1, 174, 4, 344], [1, 2, 340, 8], [5, 170, 340, 344], [5, 170, 4, 348], [337, 2, 4, 488]], 'outer_group': '384.16843', 'outer_hash': 16843, 'outer_nilpotent': True, 'outer_order': 384, 'outer_permdeg': 15, 'outer_perms': [1680, 193198079760, 560551663464, 2446578984, 288848892268], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_6.D_4^2', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 20, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2, 2], 'quasisimple': False, 'rank': 4, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 16], [2, 8], [4, 4], [6, 8], [12, 4], [24, 4]], 'representations': {'PC': {'code': 3541704130793124666366399981116269276035467, 'gens': [1, 2, 3, 4], 'pres': [7, -2, -2, -2, -2, -2, -3, -7, 2352, 6499, 9306, 80, 16244, 11491, 102, 10757, 13452, 166, 14125]}, 'GLZN': {'d': 2, 'p': 70, 'gens': [343701, 9982041, 4461463, 9947029, 516986, 344499, 23667069]}, 'Perm': {'d': 20, 'gens': [140914996122705966, 244064350274169600, 1, 392034417738163201, 499824708218035200, 43545600, 50646]}}, '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': 'D_{84}:C_2^2', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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, 8, 32], [1, 2, 4, 8, 34], [17, 2, 4, 8, 32], [1, 2, 28, 8, 32], [1, 2, 4, 24, 1312], [1, 2, 4, 8, 1312], [897, 2, 900, 8, 928], [1, 2, 4, 8, 1184], [1, 2, 20, 8, 32], [683, 696, 686, 8, 34], [897, 2, 900, 8, 32], [1, 2, 388, 8, 32], [17, 18, 20, 8, 32], [1, 2, 4, 8, 48]], 'aut_group': None, 'aut_hash': None, 'aut_nilpotency_class': None, 'aut_nilpotent': None, 'aut_order': 96768, 'aut_permdeg': None, 'aut_perms': None, 'aut_phi_ratio': None, 'aut_solvable': None, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 3, 1], [2, 6, 1, 1], [2, 6, 3, 1], [2, 14, 2, 1], [2, 42, 6, 1], [3, 2, 1, 1], [4, 2, 1, 1], [4, 2, 3, 1], [4, 3, 2, 1], [4, 6, 3, 1], [4, 14, 6, 1], [4, 42, 2, 1], [6, 2, 1, 1], [6, 4, 3, 1], [6, 28, 2, 1], [7, 2, 3, 1], [12, 4, 1, 1], [12, 4, 3, 1], [12, 28, 6, 1], [14, 2, 3, 1], [14, 4, 9, 1], [14, 6, 6, 1], [14, 12, 9, 1], [21, 4, 3, 1], [28, 2, 6, 1], [28, 4, 9, 1], [28, 6, 6, 1], [28, 12, 9, 1], [42, 4, 3, 1], [42, 8, 9, 1], [84, 4, 6, 1], [84, 8, 9, 1]], 'aut_supersolvable': None, 'aut_tex': None, '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, 1], [2, 2, 3], [2, 6, 4], [2, 14, 2], [2, 42, 6], [3, 2, 1], [4, 2, 4], [4, 3, 2], [4, 6, 3], [4, 14, 6], [4, 42, 2], [6, 2, 1], [6, 4, 3], [6, 28, 2], [7, 2, 3], [12, 4, 4], [12, 28, 6], [14, 2, 3], [14, 4, 9], [14, 6, 6], [14, 12, 9], [21, 4, 3], [28, 2, 6], [28, 4, 9], [28, 6, 6], [28, 12, 9], [42, 4, 3], [42, 8, 9], [84, 4, 6], [84, 8, 9]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '672.1271', 'commutator_count': 1, 'commutator_label': '42.6', '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', '7.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 11566, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 3], [2, 6, 1, 4], [2, 14, 1, 2], [2, 42, 1, 6], [3, 2, 1, 1], [4, 2, 1, 4], [4, 3, 2, 1], [4, 6, 1, 3], [4, 14, 1, 6], [4, 42, 1, 2], [6, 2, 1, 1], [6, 4, 1, 3], [6, 28, 1, 2], [7, 2, 3, 1], [12, 4, 1, 4], [12, 28, 1, 6], [14, 2, 3, 1], [14, 4, 3, 3], [14, 6, 6, 1], [14, 12, 3, 3], [21, 4, 3, 1], [28, 2, 6, 1], [28, 4, 3, 3], [28, 6, 6, 1], [28, 12, 3, 3], [42, 4, 3, 1], [42, 8, 3, 3], [84, 4, 6, 1], [84, 8, 3, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 13332480000, 'exponent': 84, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3, 7], 'factors_of_order': [2, 3, 7], 'faithful_reps': [[8, 1, 6]], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '672.1271', 'hash': 11566, 'hyperelementary': 2, 'inner_abelian': None, 'inner_cyclic': None, 'inner_exponent': None, 'inner_gen_orders': None, 'inner_gens': None, 'inner_hash': None, 'inner_nilpotent': None, 'inner_order': 672, 'inner_split': None, 'inner_tex': 'C_{21}:C_2^5', 'inner_used': None, 'irrC_degree': 8, 'irrQ_degree': 48, 'irrQ_dim': 96, 'irrR_degree': 8, 'irrep_stats': [[1, 32], [2, 64], [4, 38], [8, 7]], 'label': '1344.11566', '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': 'C84.C2^4', '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, 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': 34, 'number_characteristic_subgroups': 40, 'number_conjugacy_classes': 141, 'number_divisions': 76, 'number_normal_subgroups': 528, 'number_subgroup_autclasses': 404, 'number_subgroup_classes': 1620, 'number_subgroups': 11652, 'old_label': None, 'order': 1344, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 311], [3, 2], [4, 200], [6, 70], [7, 6], [12, 184], [14, 186], [21, 12], [28, 192], [42, 84], [84, 96]], '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': '144.195', 'outer_hash': None, 'outer_nilpotent': None, 'outer_order': 144, 'outer_permdeg': None, 'outer_perms': None, 'outer_solvable': None, 'outer_supersolvable': None, 'outer_tex': 'C_6^2:C_2^2', 'pc_rank': 5, 'perfect': False, 'permutation_degree': 26, '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, 16], [6, 16], [8, 2], [12, 8], [48, 2]], 'representations': {'PC': {'code': 5559847065097708954379003499261975844813588965899, 'gens': [1, 2, 3, 4, 6], 'pres': [8, -2, -2, -2, -2, -2, 2, -3, -7, 137, 211, 91, 45317, 1165, 15765, 141, 28678, 17942, 222, 18455]}, 'Perm': {'d': 26, 'gens': [621574835364366654960196, 358828940499169, 4579447041886, 5987254304875, 6767426431180, 8698611191114, 6758061133824000, 16754357281155028254720000]}}, '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_{84}.C_2^4', 'transitive_degree': 336, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'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}
