-
gps_subgroup_search • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'ambient': '864.689', 'ambient_counter': 689, 'ambient_order': 864, 'ambient_tex': '(C_3\\times A_4):C_{24}', 'central': False, 'central_factor': False, 'centralizer_order': 4, 'characteristic': True, 'core_order': 288, 'counter': 3, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '864.689.3.a1.a1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '3.a1.a1', 'outer_equivalence': False, 'perfect': False, 'proper': True, 'quotient': '3.1', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 1, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 3, 'quotient_simple': True, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_3', 'simple': False, 'solvable': True, 'special_labels': [], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '288.402', 'subgroup_hash': 402, 'subgroup_order': 288, 'subgroup_tex': 'C_{12}.S_4', 'supersolvable': False, 'sylow': 0}
-
gps_subgroup_data • Show schema
Hide schema
{'ambient': '864.689', 'aut_centralizer_order': 1, 'aut_label': '3.a1', 'aut_quo_index': 1, 'aut_stab_index': 1, 'aut_weyl_group': '1728.46116', 'aut_weyl_index': 1, 'centralizer': '216.a1.a1', 'complements': ['288.b1.a1', '288.d1.a1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['6.b1.a1', '9.a1.a1', '9.c1.a1', '12.h1.a1'], 'core': '3.a1.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [4101, 3023, 5717, 4217, 5284, 6482, 4665, 1271], 'generators': [3, 216, 144, 6, 432, 12, 24], 'label': '864.689.3.a1.a1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '3.a1.a1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['6.b1.a1'], 'normalizer': '1.a1.a1', 'old_label': '3.a1.a1', 'projective_image': '216.92', 'quotient_action_image': '3.1', 'quotient_action_kernel': '1.1', 'quotient_action_kernel_order': 1, 'quotient_fusion': None, 'short_label': '3.a1.a1', 'subgroup_fusion': None, 'weyl_group': '216.92'}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 8, 24, 144], [1, 8, 120, 144], [1, 16, 264, 144], [5, 8, 24, 144], [3, 8, 24, 144], [17, 8, 240, 216], [1, 104, 24, 144], [97, 8, 24, 144], [145, 224, 24, 144], [1, 80, 24, 144]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 72, 'aut_perms': [119104705619027829844289178024814194513020478876369172124638547721852809628426350200428029393631480, 6687643986850360475654769195338544889865432588698746975766707676481998180378565267642745007053430261, 8660026160654545993497270522209617247234983506768878788514676312025730343415543563822165298666347285781, 850828275212888371529444618539791166389365013336357835391274953932372908499614381585320177908853056816, 54362126952738340082700119758818943227791612403186596018643932385778641690507318750799517481762388994821, 4179761570608096679640365515766386688679288070613192003882467622360053352082839731583305361176904749, 20703151596379842745272631824867081493094904514533303865098858161807998727690135690723645150657655060576, 7786418879759582050403610847495620409648400786952607025511847971440210103549669995229765083468794493090, 6608255365820604288783102863724654969802626227039130111707139180693950712717615834214207398259609069], 'aut_phi_ratio': 18.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 3, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 3, 1], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 6, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 8, 3], [4, 1, 2], [4, 3, 2], [6, 2, 1], [6, 6, 2], [6, 8, 3], [8, 18, 8], [12, 2, 2], [12, 6, 2], [12, 8, 6]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '72.43', 'commutator_count': 1, 'commutator_label': '36.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1'], 'composition_length': 7, 'conjugacy_classes_known': True, 'counter': 402, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 8, 1, 3], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 6, 1, 2], [6, 8, 1, 3], [8, 18, 4, 2], [12, 2, 2, 1], [12, 6, 2, 1], [12, 8, 2, 3]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 6720, 'exponent': 24, 'exponents_of_order': [5, 2], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 2]], 'familial': False, 'frattini_label': '4.1', 'frattini_quotient': '72.43', 'hash': 402, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [2, 3, 6, 2], 'inner_gens': [[1, 16, 264, 144], [17, 8, 240, 216], [193, 224, 24, 144], [1, 80, 24, 144]], 'inner_hash': 43, 'inner_nilpotent': False, 'inner_order': 72, 'inner_split': True, 'inner_tex': 'C_3:S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 8], [2, 16], [3, 8], [6, 4]], 'label': '288.402', 'linC_count': 72, 'linC_degree': 5, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 7, 'linQ_degree_count': 6, 'linQ_dim': 7, 'linQ_dim_count': 6, 'linR_count': 18, 'linR_degree': 7, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C12.S4', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 17, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 36, 'number_divisions': 23, 'number_normal_subgroups': 25, 'number_subgroup_autclasses': 52, 'number_subgroup_classes': 68, 'number_subgroups': 248, 'old_label': None, 'order': 288, 'order_factorization_type': 32, 'order_stats': [[1, 1], [2, 7], [3, 26], [4, 8], [6, 38], [8, 144], [12, 64]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 6, 'outer_gen_orders': [2, 2, 6], 'outer_gen_pows': [0, 0, 0], 'outer_gens': [[5, 8, 24, 144], [1, 16, 168, 144], [3, 112, 264, 144]], 'outer_group': '24.14', 'outer_hash': 14, 'outer_nilpotent': False, 'outer_order': 24, 'outer_permdeg': 7, 'outer_perms': [16, 127, 847], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times D_6', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 15, 'pgroup': 0, 'primary_abelian_invariants': [8], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 9], [3, 2], [4, 5], [6, 3], [12, 2]], 'representations': {'PC': {'code': 22675231374012014717598665098, 'gens': [1, 4, 5, 7], 'pres': [7, 2, 2, 2, 3, 2, 3, 2, 14, 36, 451, 9244, 1075, 102, 4037, 1350]}, 'GLZN': {'d': 2, 'p': 20, 'gens': [11293, 140017, 24003, 72009, 60207, 130311, 540]}, 'Perm': {'d': 15, 'gens': [94447180922, 194123381760, 288369849600, 843, 1440, 7, 16]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [8], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{12}.S_4', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': False, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '24.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 12, 'aut_gen_orders': [2, 2, 2, 2, 3, 3, 3, 2, 2], 'aut_gens': [[1, 24, 72, 432], [17, 168, 360, 432], [1, 48, 792, 432], [13, 24, 72, 432], [19, 24, 72, 432], [169, 24, 504, 216], [1, 312, 72, 432], [145, 24, 72, 432], [433, 456, 72, 432], [1, 240, 72, 432]], 'aut_group': '1728.46116', 'aut_hash': 46116, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 1728, 'aut_permdeg': 78, 'aut_perms': [5295548843217170472400478212322678748389083704562030217064137866433953882632933937238947123984090837285902799096879, 2009719810372223290761303414372549086585549392737147172256042050843049673350342685675776509491474133903709471577194, 7354711702814386350602789702516768360781856303454664007780383076804726870995062508243264185673679750256925441469996, 10038694049430935828633075069655415461582246601797231161900599558031598055800490897540201103928863145009630947441573, 442095442189494481704099712211241569891177668764312773797770211505049281282881907288053683263090230497711541060269, 67915382970325953219339732478674543960960055042919592002643987916047985117331760576063999773722716576301851015185, 10682433842927728853391538386954479030079016517468878529258272976956126034638217356163722687778412602464696540182484, 8408069569561729557829825004636011199992312418650861600172119611296238779939642984099475821267807011435865738702793, 132012684163470527824591884274691431912899011054917669233056324178126554784360936797504613936880508343150569678225], 'aut_phi_ratio': 6.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 3, 2, 1], [3, 24, 1, 1], [3, 24, 2, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 3, 2, 3], [6, 6, 1, 2], [6, 6, 2, 2], [6, 24, 1, 1], [6, 24, 2, 1], [8, 18, 4, 2], [12, 2, 2, 1], [12, 3, 4, 2], [12, 6, 2, 1], [12, 6, 4, 1], [12, 24, 2, 1], [12, 24, 4, 1], [24, 18, 8, 2]], 'aut_supersolvable': False, 'aut_tex': 'C_2^2\\times C_6^2:D_6', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 2, 'autcent_group': '4.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^2', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 12, 'autcentquo_group': '432.523', 'autcentquo_hash': 523, 'autcentquo_nilpotent': False, 'autcentquo_order': 432, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_6^2:D_6', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 3, 2], [3, 2, 1], [3, 3, 2], [3, 24, 3], [4, 1, 2], [4, 3, 2], [6, 2, 1], [6, 3, 6], [6, 6, 6], [6, 24, 3], [8, 18, 8], [12, 2, 2], [12, 3, 8], [12, 6, 6], [12, 24, 6], [24, 18, 16]], 'center_label': '4.1', 'center_order': 4, 'central_product': False, 'central_quotient': '216.92', 'commutator_count': 1, 'commutator_label': '36.11', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '2.1', '2.1', '3.1', '3.1', '3.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 689, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 3, 1, 2], [3, 2, 1, 1], [3, 3, 2, 1], [3, 24, 1, 1], [3, 24, 2, 1], [4, 1, 2, 1], [4, 3, 2, 1], [6, 2, 1, 1], [6, 3, 2, 3], [6, 6, 1, 2], [6, 6, 2, 2], [6, 24, 1, 1], [6, 24, 2, 1], [8, 18, 4, 2], [12, 2, 2, 1], [12, 3, 4, 2], [12, 6, 2, 1], [12, 6, 4, 1], [12, 24, 2, 1], [12, 24, 4, 1], [24, 18, 8, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 144, 'exponent': 24, 'exponents_of_order': [5, 3], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3], 'faithful_reps': [[6, 0, 6]], 'familial': False, 'frattini_label': '12.2', 'frattini_quotient': '72.42', 'hash': 689, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 12, 'inner_gen_orders': [6, 3, 6, 2], 'inner_gens': [[1, 336, 792, 432], [193, 24, 720, 648], [577, 672, 72, 432], [1, 240, 72, 432]], 'inner_hash': 92, 'inner_nilpotent': False, 'inner_order': 216, 'inner_split': True, 'inner_tex': 'C_3^2:S_4', 'inner_used': [1, 2, 3], 'irrC_degree': 6, 'irrQ_degree': 12, 'irrQ_dim': 12, 'irrR_degree': 12, 'irrep_stats': [[1, 24], [2, 12], [3, 24], [6, 16]], 'label': '864.689', 'linC_count': 6, 'linC_degree': 6, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 10, 'linQ_degree_count': 4, 'linQ_dim': 10, 'linQ_dim_count': 2, 'linR_count': 6, 'linR_degree': 8, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': '(C3*A4):C24', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 31, 'number_characteristic_subgroups': 26, 'number_conjugacy_classes': 76, 'number_divisions': 31, 'number_normal_subgroups': 26, 'number_subgroup_autclasses': 115, 'number_subgroup_classes': 115, 'number_subgroups': 580, 'old_label': None, 'order': 864, 'order_factorization_type': 33, 'order_stats': [[1, 1], [2, 7], [3, 80], [4, 8], [6, 128], [8, 144], [12, 208], [24, 288]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2, 2, 2], 'outer_gen_pows': [0, 0, 16], 'outer_gens': [[17, 168, 360, 432], [19, 24, 72, 432], [13, 312, 72, 432]], 'outer_group': '8.5', 'outer_hash': 5, 'outer_nilpotent': True, 'outer_order': 8, 'outer_permdeg': 6, 'outer_perms': [1, 6, 120], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 21, 'pgroup': 0, 'primary_abelian_invariants': [8, 3], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [2, 5], [3, 2], [4, 5], [6, 7], [8, 2], [12, 6], [24, 2]], 'representations': {'PC': {'code': 14112253796389535278866357272522050133055776538, 'gens': [1, 5, 6, 8], 'pres': [8, 2, 2, 2, 3, 3, 2, 3, 2, 16, 41, 66, 13444, 6252, 1700, 1588, 38021, 1477, 141, 16134, 1767]}, 'Perm': {'d': 21, 'gens': [121667518206271489, 16313, 45962678361600, 68349217305600, 128047474114611932, 98499, 2439304381882368000, 5109094217170944000]}}, 'schur_multiplier': [6], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [24], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': '(C_3\\times A_4):C_{24}', 'transitive_degree': 72, 'wreath_data': None, 'wreath_product': False}
-
gps_groups • Show schema
Hide schema
{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '3.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 2, 'aut_gen_orders': [2], 'aut_gens': [[1], [2]], 'aut_group': '2.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 2, 'aut_permdeg': 2, 'aut_perms': [1], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_2', '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': 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], [3, 1, 2]], 'center_label': '3.1', 'center_order': 3, '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': ['3.1'], 'composition_length': 1, 'conjugacy_classes_known': True, 'counter': 1, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [3, 1, 2, 1]], 'element_repr_type': 'PC', 'elementary': 3, 'eulerian_function': 1, 'exponent': 3, 'exponents_of_order': [1], 'factors_of_aut_order': [2], 'factors_of_order': [3], 'faithful_reps': [[1, 0, 2]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3.1', 'hash': 1, 'hyperelementary': 3, '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': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 3]], 'label': '3.1', 'linC_count': 2, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 2, 'linQ_degree_count': 1, 'linQ_dim': 2, 'linQ_dim_count': 1, 'linR_count': 1, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C3', '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': 3, 'number_divisions': 2, 'number_normal_subgroups': 2, 'number_subgroup_autclasses': 2, 'number_subgroup_classes': 2, 'number_subgroups': 2, 'old_label': None, 'order': 3, 'order_factorization_type': 1, 'order_stats': [[1, 1], [3, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [0], 'outer_gens': [[2]], 'outer_group': '2.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 2, 'outer_permdeg': 2, 'outer_perms': [1], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 3, 'pgroup': 3, 'primary_abelian_invariants': [3], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1]], 'representations': {'PC': {'code': 0, 'gens': [1], 'pres': [1, -3]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [7]}, 'Lie': [{'d': 1, 'q': 3, 'gens': [3], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 2, 'gens': [7]}, 'Perm': {'d': 3, 'gens': [4]}}, 'schur_multiplier': [], 'semidirect_product': False, 'simple': True, 'smith_abelian_invariants': [3], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_3', 'transitive_degree': 3, 'wreath_data': None, 'wreath_product': False}
