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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '39930.c', 'ambient_counter': 3, 'ambient_order': 39930, 'ambient_tex': 'C_5\\times C_{11}\\wr S_3', 'central': False, 'central_factor': False, 'centralizer_order': 55, 'characteristic': True, 'core_order': 3993, 'counter': 6, 'cyclic': False, 'direct': False, 'hall': 33, 'label': '39930.c.10.a1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '10.a1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '10.2', 'quotient_Agroup': True, 'quotient_abelian': True, 'quotient_cyclic': True, 'quotient_hash': 2, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 10, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'C_{10}', 'simple': False, 'solvable': True, 'special_labels': ['C2', 'C2'], 'split': True, 'standard_generators': False, 'stem': False, 'subgroup': '3993.6', 'subgroup_hash': 6, 'subgroup_order': 3993, 'subgroup_tex': 'C_{11}\\wr C_3', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '39930.c', 'aut_centralizer_order': None, 'aut_label': '10.a1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '726.a1', 'complements': ['3993.a1'], 'conjugacy_class_count': 1, 'contained_in': ['2.a1', '5.a1'], 'contains': ['30.a1', '110.a1', '1210.a1'], 'core': '10.a1', 'coset_action_label': None, 'count': 1, 'diagramx': [5443, 5173, 1602, 3276], 'generators': [107403653, 119183120, 79720323, 99207417], 'label': '39930.c.10.a1', 'mobius_quo': 0, 'mobius_sub': 1, 'normal_closure': '10.a1', 'normal_contained_in': ['2.a1', '5.a1'], 'normal_contains': ['30.a1', '110.a1'], 'normalizer': '1.a1', 'old_label': '10.a1', 'projective_image': '3630.i', 'quotient_action_image': '2.1', 'quotient_action_kernel': '5.1', 'quotient_action_kernel_order': 5, 'quotient_fusion': None, 'short_label': '10.a1', 'subgroup_fusion': None, 'weyl_group': '726.5'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '33.1', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 1320, 'aut_gen_orders': [10, 10, 20, 20], 'aut_gens': [[1, 33, 363], [2693, 957, 1617], [3818, 198, 2046], [2216, 1386, 825], [3572, 528, 2409]], 'aut_group': None, 'aut_hash': 918826766112171845, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 290400, 'aut_permdeg': 252, 'aut_perms': [29636313145691704291517294188584874896218751826283087193457911274349292167431043320267188235078467450542649545711782489292684062811471416555401726814196824690752479672013251555382104492589978436767944302825405251764689877888613618486055553143705722567299241169824817734429550387772579163344704591566862287707999068578957752203360747462933882209026783300487022767328880503128004471438964285443119678890255580366252282525943078977967034857714983522515804324995740595191298455399389534056519398994247, 88785984984210064693975808233413214609170928452490515548882308074464443758045527984302719718635377222704800038242461437296775187731890346401271812331419328547530120000981783614813563032209804694986898766519494655043294274072934622486558517150610009213528585544772656809069615768567051110951880819826191944767774386787154348183580691962949808291562927146342342480129558295146791211613718786528917196214591995987587035204865841607927101754200474084174162913253667614264021440709622084557959653921595, 72279343452914659324610768799936063551109931941583911029144385091727698211767655346293705554553223102744155963930229846683524911719854293827766321744898284328735263456708874994046677272798378141710653740677345770090933767505216964914441216858524085905449526117369245756605940482469820694103684393022244700738101409130781959066159332076258049962327966471354863760320195299259128970095000624849304440064968359004985417382250796327943385533810800591795331481540044814938619508179996142309430050846428, 78577254208074680388653909208999683013265317803877357021734386673447361428096978408153347167300055316013038431717623624686793533501708878401052300892370514572867298020710509821035287009921247006390562138010394028653713903811398478713209347719041163721844420041829653188696759344258115734555632482808089631807051668959632098297418408781984736348991373150959036206204466964649493047879827693561790891158932859274150197068577099451448658341285080793118104787091281691495403699380511985423092324624779], 'aut_phi_ratio': 120.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [3, 121, 2, 1], [11, 1, 10, 1], [11, 3, 40, 1], [11, 3, 400, 1], [33, 121, 20, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{60}.C_5.C_2^3', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 10, 'autcent_group': '10.2', 'autcent_hash': 2, 'autcent_nilpotent': True, 'autcent_order': 10, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_{10}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 1320, 'autcentquo_group': '29040.bc', 'autcentquo_hash': 1762754374357461501, 'autcentquo_nilpotent': False, 'autcentquo_order': 29040, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{121}:C_2', 'cc_stats': [[1, 1, 1], [3, 121, 2], [11, 1, 10], [11, 3, 440], [33, 121, 20]], 'center_label': '11.1', 'center_order': 11, 'central_product': True, 'central_quotient': '363.2', 'commutator_count': 1, 'commutator_label': '121.2', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['3.1', '11.1', '11.1', '11.1'], 'composition_length': 4, 'conjugacy_classes_known': True, 'counter': 6, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['363.2', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [3, 121, 2, 1], [11, 1, 10, 1], [11, 3, 10, 44], [33, 121, 20, 1]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 48, 'exponent': 33, 'exponents_of_order': [3, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [3, 11], 'faithful_reps': [[3, 0, 400]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '3993.6', 'hash': 6, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 33, 'inner_gen_orders': [3, 11, 11], 'inner_gens': [[1, 660, 627], [3730, 33, 363], [100, 33, 363]], 'inner_hash': 2, 'inner_nilpotent': False, 'inner_order': 363, 'inner_split': True, 'inner_tex': 'C_{11}^2:C_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 30, 'irrQ_dim': 30, 'irrR_degree': 6, 'irrep_stats': [[1, 33], [3, 440]], 'label': '3993.6', 'linC_count': 400, 'linC_degree': 3, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 30, 'linQ_degree_count': 40, 'linQ_dim': 30, 'linQ_dim_count': 40, 'linR_count': 200, 'linR_degree': 6, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': False, 'monomial': True, 'name': 'C11wrC3', 'ngens': 4, 'nilpotency_class': -1, 'nilpotent': False, 'normal_counts': [0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 6, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 473, 'number_divisions': 48, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 12, 'number_subgroup_classes': 96, 'number_subgroups': 512, 'old_label': None, 'order': 3993, 'order_factorization_type': 31, 'order_stats': [[1, 1], [3, 242], [11, 1330], [33, 2420]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 40, 'outer_gen_orders': [2, 10, 40], 'outer_gen_pows': [32, 0, 0], 'outer_gens': [[10, 660, 627], [8, 660, 990], [1, 825, 3432]], 'outer_group': '800.952', 'outer_hash': 952, 'outer_nilpotent': True, 'outer_order': 800, 'outer_permdeg': 20, 'outer_perms': [39916800, 13516128494668890, 878906256441706080], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_8:C_{10}^2', 'pc_rank': 3, 'perfect': False, 'permutation_degree': 33, 'pgroup': 0, 'primary_abelian_invariants': [3, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 1], [2, 1], [10, 1], [20, 1], [30, 44]], 'representations': {'PC': {'code': '7185570867691999', 'gens': [1, 3, 4], 'pres': [4, -3, -11, -11, 11, 12, 7922, 10035]}, 'Lie': [{'d': 1, 'q': 1331, 'family': 'ASigmaL'}], 'GLZq': {'d': 2, 'q': 121, 'gens': [119507884, 120309146, 1757161, 1932613]}, 'Perm': {'d': 33, 'gens': [5975817900939513912271439485992960000, 1901394391467741686218740989968151616, 375563241578020631616, 2631308369336935812581601838730688000]}}, 'schur_multiplier': [11], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [33], 'solvability_type': 8, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}\\wr C_3', 'transitive_degree': 33, 'wreath_data': ['C_{11}', 'C_3', '3T1'], 'wreath_product': True}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '110.6', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 660, 'aut_gen_orders': [12, 10, 110, 22, 20], 'aut_gens': [[157669049, 107403653, 177644600, 162983682], [204841060, 127364649, 41234480, 173459955], [106434972, 9701895, 40746003, 122573179], [68972349, 68804917, 177644600, 25931986], [146379514, 107458466, 79720323, 28024231], [185186238, 87008993, 177156123, 67975517]], 'aut_group': None, 'aut_hash': 3408281614888932655, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 290400, 'aut_permdeg': 47, 'aut_perms': [185900222615568644856876809332618281893810635637220250490113, 76563585737373329395084132466750670189248870604569237947395, 38269227270162736545075254955030700535938036681952052511386, 185898347622074758438859139742570083473162740477562973640765, 75873590595994049670962049582514064516819481628702510255739], 'aut_phi_ratio': 30.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 33, 1, 1], [3, 242, 1, 1], [5, 1, 4, 1], [10, 33, 4, 1], [11, 1, 10, 1], [11, 3, 10, 1], [11, 3, 100, 1], [11, 6, 5, 1], [11, 6, 10, 1], [11, 6, 50, 1], [11, 6, 100, 1], [15, 242, 4, 1], [22, 33, 10, 2], [22, 33, 100, 1], [33, 242, 10, 1], [55, 1, 40, 1], [55, 3, 40, 1], [55, 3, 400, 1], [55, 6, 20, 1], [55, 6, 40, 1], [55, 6, 200, 1], [55, 6, 400, 1], [110, 33, 40, 2], [110, 33, 400, 1], [165, 242, 40, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{15}.C_{10}.C_2^4', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 20, 'autcent_group': '40.9', 'autcent_hash': 9, 'autcent_nilpotent': True, 'autcent_order': 40, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2\\times C_{20}', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 330, 'autcentquo_group': '7260.bg', 'autcentquo_hash': 7237787727408842954, 'autcentquo_nilpotent': False, 'autcentquo_order': 7260, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'C_{11}^2:(S_3\\times C_{10})', 'cc_stats': [[1, 1, 1], [2, 33, 1], [3, 242, 1], [5, 1, 4], [10, 33, 4], [11, 1, 10], [11, 3, 110], [11, 6, 165], [15, 242, 4], [22, 33, 120], [33, 242, 10], [55, 1, 40], [55, 3, 440], [55, 6, 660], [110, 33, 480], [165, 242, 40]], 'center_label': '55.2', 'center_order': 55, 'central_product': True, 'central_quotient': '726.5', 'commutator_count': 1, 'commutator_label': '363.2', 'complements_known': True, 'complete': False, 'complex_characters_known': False, 'composition_factors': ['2.1', '3.1', '5.1', '11.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['11.1', 1], ['5.1', 1], ['726.5', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 33, 1, 1], [3, 242, 1, 1], [5, 1, 4, 1], [10, 33, 4, 1], [11, 1, 10, 1], [11, 3, 10, 11], [11, 6, 5, 1], [11, 6, 10, 16], [15, 242, 4, 1], [22, 33, 10, 12], [33, 242, 10, 1], [55, 1, 40, 1], [55, 3, 40, 11], [55, 6, 20, 1], [55, 6, 40, 16], [110, 33, 40, 12], [165, 242, 40, 1]], 'element_repr_type': 'GLZq', 'elementary': 1, 'eulerian_function': 2592, 'exponent': 330, 'exponents_of_order': [3, 1, 1, 1], 'factors_of_aut_order': [2, 3, 5, 11], 'factors_of_order': [2, 3, 5, 11], 'faithful_reps': [[3, 0, 800], [6, 0, 600]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '39930.c', 'hash': 164722554699628861, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 66, 'inner_gen_orders': [22, 3, 11, 11], 'inner_gens': [[157669049, 107946943, 178453848, 162983682], [145464875, 107403653, 79720323, 26908853], [158639348, 10441689, 177644600, 162983682], [157669049, 107556718, 177644600, 162983682]], 'inner_hash': 5, 'inner_nilpotent': False, 'inner_order': 726, 'inner_split': True, 'inner_tex': 'C_{11}^2:S_3', 'inner_used': [1, 2], 'irrC_degree': 3, 'irrQ_degree': 120, 'irrQ_dim': None, 'irrR_degree': None, 'irrep_stats': [[1, 110], [2, 55], [3, 1100], [6, 825]], 'label': '39930.c', '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': False, 'metacyclic': False, 'monomial': True, 'name': 'C5*C11wrS3', '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, 0, 0, 0, 0, 0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 28, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 2090, 'number_divisions': 90, 'number_normal_subgroups': 16, 'number_subgroup_autclasses': 68, 'number_subgroup_classes': 192, 'number_subgroups': 2520, 'old_label': None, 'order': 39930, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 33], [3, 242], [5, 4], [10, 132], [11, 1330], [15, 968], [22, 3960], [33, 2420], [55, 5320], [110, 15840], [165, 9680]], 'outer_abelian': True, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 20, 'outer_gen_orders': [2, 10, 20], 'outer_gen_pows': [107403653, 107403653, 1771562], 'outer_gens': [[205318889, 107403653, 41234480, 46396013], [48991432, 107403653, 118694643, 182959319], [79720354, 107403653, 42043728, 184242415]], 'outer_group': '400.201', 'outer_hash': 201, 'outer_nilpotent': True, 'outer_order': 400, 'outer_permdeg': 18, 'outer_perms': [1307674368000, 355693696248960, 13451961633], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2\\times C_{10}\\times C_{20}', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 38, 'pgroup': 0, 'primary_abelian_invariants': [2, 5, 11], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': False, 'ratrep_stats': [[1, 2], [2, 1], [4, 2], [8, 1], [10, 2], [20, 1], [30, 23], [40, 2], [60, 16], [80, 1], [120, 23], [240, 16]], 'representations': {'PC': {'code': '94865677111217709399317494488190046815441091939', 'gens': [1, 3, 4, 5], 'pres': [6, 2, 11, 3, 11, 5, 11, 12, 78014, 132074, 887043, 3975, 20986, 178, 60497]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12531822321003912, 36596619999581411, 28745646345613891, 42771567939938742, 19063078487671420, 17298483428108842]}, 'GLZq': {'d': 2, 'q': 121, 'gens': [106969989, 47832174, 1771617, 41081349, 196643382, 1771681]}, 'Perm': {'d': 38, 'gens': [29462864638184677479536993474525075498035920, 90, 96402800143457235296762783534192263967969760, 213648602383098892524023385440526594412018560, 57807522871758521146359618321510186331893840, 72636314234587979715969788280020836147200]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [110], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_5\\times C_{11}\\wr S_3', 'transitive_degree': 165, 'wreath_data': None, 'wreath_product': False}
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{'Agroup': True, 'Zgroup': True, 'abelian': True, 'abelian_quotient': '10.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': True, 'aut_cyclic': True, 'aut_derived_length': 1, 'aut_exponent': 4, 'aut_gen_orders': [4], 'aut_gens': [[1], [7]], 'aut_group': '4.1', 'aut_hash': 1, 'aut_nilpotency_class': 1, 'aut_nilpotent': True, 'aut_order': 4, 'aut_permdeg': 4, 'aut_perms': [9], 'aut_phi_ratio': 1.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4', 'autcent_abelian': True, 'autcent_cyclic': True, 'autcent_exponent': 4, 'autcent_group': '4.1', 'autcent_hash': 1, 'autcent_nilpotent': True, 'autcent_order': 4, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4', '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], [5, 1, 4], [10, 1, 4]], 'center_label': '10.2', 'center_order': 10, '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', '5.1'], 'composition_length': 2, 'conjugacy_classes_known': True, 'counter': 2, 'cyclic': True, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [5, 1, 4, 1], [10, 1, 4, 1]], 'element_repr_type': 'PC', 'elementary': 10, 'eulerian_function': 1, 'exponent': 10, 'exponents_of_order': [1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 5], 'faithful_reps': [[1, 0, 4]], 'familial': True, 'frattini_label': '1.1', 'frattini_quotient': '10.2', 'hash': 2, 'hyperelementary': 10, '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': 4, 'irrQ_dim': 4, 'irrR_degree': 2, 'irrep_stats': [[1, 10]], 'label': '10.2', 'linC_count': 4, 'linC_degree': 1, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 4, 'linQ_degree_count': 1, 'linQ_dim': 4, 'linQ_dim_count': 1, 'linR_count': 2, 'linR_degree': 2, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C10', 'ngens': 2, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [0, 0, 0, 0], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 4, 'number_characteristic_subgroups': 4, 'number_conjugacy_classes': 10, 'number_divisions': 4, 'number_normal_subgroups': 4, 'number_subgroup_autclasses': 4, 'number_subgroup_classes': 4, 'number_subgroups': 4, 'old_label': None, 'order': 10, 'order_factorization_type': 11, 'order_stats': [[1, 1], [2, 1], [5, 4], [10, 4]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [4], 'outer_gen_pows': [0], 'outer_gens': [[7]], 'outer_group': '4.1', 'outer_hash': 1, 'outer_nilpotent': True, 'outer_order': 4, 'outer_permdeg': 4, 'outer_perms': [9], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4', 'pc_rank': 1, 'perfect': False, 'permutation_degree': 7, 'pgroup': 0, 'primary_abelian_invariants': [2, 5], 'quasisimple': False, 'rank': 1, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 2], [4, 2]], 'representations': {'PC': {'code': 83, 'gens': [1], 'pres': [2, -2, -5, 4]}, 'GLZ': {'b': 3, 'd': 4, 'gens': [16717348]}, 'GLFp': {'d': 2, 'p': 5, 'gens': [131, 504]}, 'Perm': {'d': 7, 'gens': [720, 96]}}, 'schur_multiplier': [], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [10], 'solvability_type': 0, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_{10}', 'transitive_degree': 10, 'wreath_data': None, 'wreath_product': False}
