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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'ambient': '960.4623', 'ambient_counter': 4623, 'ambient_order': 960, 'ambient_tex': '(C_2\\times C_{60}):Q_8', 'central': False, 'central_factor': False, 'centralizer_order': 480, 'characteristic': False, 'core_order': 120, 'counter': 25, 'cyclic': False, 'direct': False, 'hall': 0, 'label': '960.4623.8.e1', 'maximal': False, 'maximal_normal': False, 'metabelian': True, 'metacyclic': True, 'minimal': False, 'minimal_normal': False, 'nilpotent': True, 'normal': True, 'old_label': '8.e1', 'outer_equivalence': True, 'perfect': False, 'proper': True, 'quotient': '8.3', 'quotient_Agroup': False, 'quotient_abelian': False, 'quotient_cyclic': False, 'quotient_hash': 3, 'quotient_metabelian': True, 'quotient_nilpotent': True, 'quotient_order': 8, 'quotient_simple': False, 'quotient_solvable': True, 'quotient_supersolvable': True, 'quotient_tex': 'D_4', 'simple': False, 'solvable': True, 'special_labels': ['C3'], 'split': False, 'standard_generators': False, 'stem': False, 'subgroup': '120.31', 'subgroup_hash': 31, 'subgroup_order': 120, 'subgroup_tex': 'C_2\\times C_{60}', 'supersolvable': True, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '960.4623', 'aut_centralizer_order': None, 'aut_label': '8.e1', 'aut_quo_index': None, 'aut_stab_index': None, 'aut_weyl_group': None, 'aut_weyl_index': None, 'centralizer': '2.a1', 'complements': [], 'conjugacy_class_count': 2, 'contained_in': ['4.a1', '4.h1', '4.i1'], 'contains': ['16.c1', '16.d1', '24.d1', '40.e1'], 'core': '8.e1', 'coset_action_label': None, 'count': 2, 'diagramx': None, 'generators': [4, 320, 16, 240, 480], 'label': '960.4623.8.e1', 'mobius_quo': None, 'mobius_sub': None, 'normal_closure': '8.e1', 'normal_contained_in': ['4.a1'], 'normal_contains': ['16.c1', '16.d1', '24.d1', '40.e1'], 'normalizer': '1.a1', 'old_label': '8.e1', 'projective_image': None, 'quotient_action_image': None, 'quotient_action_kernel': None, 'quotient_action_kernel_order': None, 'quotient_fusion': None, 'short_label': '8.e1', 'subgroup_fusion': None, 'weyl_group': None}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': True, 'abelian_quotient': '120.31', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 2, 4, 4], 'aut_gens': [[1, 2], [1, 82], [1, 99], [1, 74], [61, 63]], 'aut_group': '64.196', 'aut_hash': 196, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 64, 'aut_permdeg': 10, 'aut_perms': [120, 806526, 408367, 22], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 1, 2, 1], [3, 1, 2, 1], [4, 1, 4, 1], [5, 1, 4, 1], [6, 1, 2, 1], [6, 1, 4, 1], [10, 1, 4, 1], [10, 1, 8, 1], [12, 1, 8, 1], [15, 1, 8, 1], [20, 1, 16, 1], [30, 1, 8, 1], [30, 1, 16, 1], [60, 1, 32, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_4^2:C_2^2', 'autcent_abelian': False, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': '64.196', 'autcent_hash': 196, 'autcent_nilpotent': True, 'autcent_order': 64, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_4^2:C_2^2', '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], [2, 1, 3], [3, 1, 2], [4, 1, 4], [5, 1, 4], [6, 1, 6], [10, 1, 12], [12, 1, 8], [15, 1, 8], [20, 1, 16], [30, 1, 24], [60, 1, 32]], 'center_label': '120.31', 'center_order': 120, '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', '2.1', '3.1', '5.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 31, 'cyclic': False, 'derived_length': 1, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['3.1', 1], ['4.1', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [3, 1, 2, 1], [4, 1, 2, 2], [5, 1, 4, 1], [6, 1, 2, 3], [10, 1, 4, 3], [12, 1, 4, 2], [15, 1, 8, 1], [20, 1, 8, 2], [30, 1, 8, 3], [60, 1, 16, 2]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 72, 'exponent': 60, 'exponents_of_order': [3, 1, 1], 'factors_of_aut_order': [2], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '2.1', 'frattini_quotient': '60.13', 'hash': 31, '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, 120]], 'label': '120.31', 'linC_count': 2304, 'linC_degree': 2, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 8, 'linQ_degree_count': 28, 'linQ_dim': 8, 'linQ_dim_count': 28, 'linR_count': 32, 'linR_degree': 3, 'maximal_subgroups_known': True, 'metabelian': True, 'metacyclic': True, 'monomial': True, 'name': 'C2*C60', 'ngens': 5, 'nilpotency_class': 1, 'nilpotent': True, 'normal_counts': [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': 16, 'number_characteristic_subgroups': 16, 'number_conjugacy_classes': 120, 'number_divisions': 24, 'number_normal_subgroups': 32, 'number_subgroup_autclasses': 24, 'number_subgroup_classes': 32, 'number_subgroups': 32, 'old_label': None, 'order': 120, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 3], [3, 2], [4, 4], [5, 4], [6, 6], [10, 12], [12, 8], [15, 8], [20, 16], [30, 24], [60, 32]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 4, 'outer_gen_orders': [2, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0], 'outer_gens': [[1, 82], [1, 99], [1, 74], [61, 63]], 'outer_group': '64.196', 'outer_hash': 196, 'outer_nilpotent': True, 'outer_order': 64, 'outer_permdeg': 10, 'outer_perms': [120, 806526, 408367, 22], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_4^2:C_2^2', 'pc_rank': 2, 'perfect': False, 'permutation_degree': 14, 'pgroup': 0, 'primary_abelian_invariants': [2, 4, 3, 5], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [2, 6], [4, 6], [8, 6], [16, 2]], 'representations': {'PC': {'code': 251909912583, 'gens': [1, 2], 'pres': [5, -2, -2, -2, -3, -5, 26, 42, 78]}, 'GLFp': {'d': 2, 'p': 61, 'gens': [10441130, 2496792]}, 'Perm': {'d': 14, 'gens': [127008000, 6227020800, 10080, 96, 40279680]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 60], 'solvability_type': 1, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{60}', 'transitive_degree': 120, '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': '80.45', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 12, 'aut_gen_orders': [4, 4, 2, 4, 4, 12, 12, 4], 'aut_gens': [[1, 2, 8, 80], [801, 282, 488, 924], [645, 242, 488, 404], [365, 726, 552, 400], [481, 486, 56, 440], [841, 762, 552, 404], [205, 282, 504, 600], [885, 282, 552, 604], [725, 722, 552, 880]], 'aut_group': None, 'aut_hash': 8133395643762616552, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 49152, 'aut_permdeg': 68, 'aut_perms': [1457750003739794565404973571100742019530922992190972170482706053965594251278845095911822268267266, 528670913502455354410144313208979579886730940086494401029973222286564594575126379761155808623878, 1146359953655958001995071149869031209376386499920175907641883638994864497473961631507757339109106, 826803602109585058227009889187690179129682192302205349964534018020926063241381651953874119866626, 1457514539296715625538815716548504106355126604850757224413992638046587123759284015972242037321068, 1408215394793316280739244384930950565877297516468020080735595756174743118211790869085780432239225, 593874456714184768450887174501612797433171700618864037671286726606948429334828730804861827357386, 269344745890456943913540824631877879126737035963893840219318437254281146089369341772734058812579], 'aut_phi_ratio': 192.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 3], [2, 1, 2, 2], [3, 2, 1, 1], [4, 2, 4, 1], [4, 2, 8, 1], [4, 12, 4, 2], [5, 1, 4, 1], [6, 2, 1, 3], [6, 2, 2, 2], [10, 1, 4, 3], [10, 1, 8, 2], [12, 2, 8, 1], [12, 2, 16, 1], [15, 2, 4, 1], [20, 2, 16, 1], [20, 2, 32, 1], [20, 12, 16, 2], [30, 2, 4, 3], [30, 2, 8, 2], [60, 2, 32, 1], [60, 2, 64, 1]], 'aut_supersolvable': True, 'aut_tex': 'C_3:(C_2^9.C_2^5)', 'autcent_abelian': True, 'autcent_cyclic': False, 'autcent_exponent': 4, 'autcent_group': None, 'autcent_hash': 1957374279625110833, 'autcent_nilpotent': True, 'autcent_order': 2048, 'autcent_solvable': True, 'autcent_split': True, 'autcent_supersolvable': True, 'autcent_tex': 'C_2^9\\times C_4', 'autcentquo_abelian': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 6, 'autcentquo_group': '24.14', 'autcentquo_hash': 14, 'autcentquo_nilpotent': False, 'autcentquo_order': 24, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2\\times D_6', 'cc_stats': [[1, 1, 1], [2, 1, 7], [3, 2, 1], [4, 2, 12], [4, 12, 8], [5, 1, 4], [6, 2, 7], [10, 1, 28], [12, 2, 24], [15, 2, 4], [20, 2, 48], [20, 12, 32], [30, 2, 28], [60, 2, 96]], 'center_label': '40.14', 'center_order': 40, 'central_product': True, 'central_quotient': '24.14', 'commutator_count': 1, 'commutator_label': '12.5', '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', '5.1'], 'composition_length': 8, 'conjugacy_classes_known': True, 'counter': 4623, 'cyclic': False, 'derived_length': 2, 'dihedral': False, 'direct_factorization': [['192.488', 1], ['5.1', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 7], [3, 2, 1, 1], [4, 2, 1, 4], [4, 2, 2, 4], [4, 12, 1, 4], [4, 12, 2, 2], [5, 1, 4, 1], [6, 2, 1, 7], [10, 1, 4, 7], [12, 2, 2, 4], [12, 2, 4, 4], [15, 2, 4, 1], [20, 2, 4, 4], [20, 2, 8, 4], [20, 12, 4, 4], [20, 12, 8, 2], [30, 2, 4, 7], [60, 2, 8, 4], [60, 2, 16, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 5208, 'exponent': 60, 'exponents_of_order': [6, 1, 1], 'factors_of_aut_order': [2, 3], 'factors_of_order': [2, 3, 5], 'faithful_reps': [], 'familial': False, 'frattini_label': '8.5', 'frattini_quotient': '120.45', 'hash': 4623, 'hyperelementary': 2, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 6, 'inner_gen_orders': [2, 2, 1, 6], 'inner_gens': [[1, 42, 8, 880], [41, 2, 8, 80], [1, 2, 8, 80], [161, 2, 8, 80]], 'inner_hash': 14, 'inner_nilpotent': False, 'inner_order': 24, 'inner_split': False, 'inner_tex': 'C_2\\times D_6', 'inner_used': [1, 2, 4], 'irrC_degree': -1, 'irrQ_degree': -1, 'irrQ_dim': -1, 'irrR_degree': -1, 'irrep_stats': [[1, 80], [2, 220]], 'label': '960.4623', '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': '(C2*C60):Q8', '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': 36, 'number_characteristic_subgroups': 46, 'number_conjugacy_classes': 300, 'number_divisions': 76, 'number_normal_subgroups': 174, 'number_subgroup_autclasses': 168, 'number_subgroup_classes': 372, 'number_subgroups': 880, 'old_label': None, 'order': 960, 'order_factorization_type': 311, 'order_stats': [[1, 1], [2, 7], [3, 2], [4, 120], [5, 4], [6, 14], [10, 28], [12, 48], [15, 8], [20, 480], [30, 56], [60, 192]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': True, 'outer_exponent': 4, 'outer_gen_orders': [4, 4, 4, 4, 2, 4, 4], 'outer_gen_pows': [0, 0, 0, 0, 0, 0, 0], 'outer_gens': [[201, 42, 56, 880], [281, 762, 552, 564], [405, 766, 552, 884], [361, 722, 488, 920], [525, 2, 72, 604], [525, 246, 552, 924], [525, 2, 24, 440]], 'outer_group': None, 'outer_hash': 5190252537470524952, 'outer_nilpotent': True, 'outer_order': 2048, 'outer_permdeg': 256, 'outer_perms': [74971960537694728968801059555293110755049314266146305554611709483049716509091704552565276169379374210512388628139198988263157864257498119473832452152265648239687376125112878036588035478869365691583597070401778004960888640397562918939385763013880823775102073628898203545914148136767692049754839384695077200437355806347562768733152920359404813074775323229466954151728801992922429339823700031801591055601564133341261719586163852979579451985334527866828581283757128676736851509170762402362273680327331635028926, 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270868611620019374787419072469914437055867238641313109657399132038779620327922466948873271523638767020202191926543943085140639574730634761743005176443348784049806033056212186221227910860037999393907022720194327551137095354556161624373813895248680839371921757731123761029799898383043842372646146445749074410981574692234251916006778744016051828852217650497819206267964591024068534560670899079118039264918805426651395208857144073264135472359147858526471335659679188635386181122441580913105234921287927225349046, 571917055508085759138938512635629539674160026514671906094622091161825347608055524346007286012803392698625830942352182902543684947959864249177889363228132716539807863180636955946811045183039277783749409392317603548740242132360345023999739045356423711112701557726709844003827000661506952285562336975051551266876670951703301193495625173676213041017503624890110037944832233291557587787434778820565089874285663553154304660732676791758895761104784117484565269983594832696998593818008825862164313591428337507587493], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_2^8.C_2^3', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 4, 5], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [2, 16], [4, 20], [8, 18], [16, 12], [32, 2]], 'representations': {'PC': {'code': 1627818105432527393365299792194518581441, 'gens': [1, 2, 4, 6], 'pres': [8, -2, -2, -2, -2, -5, -2, -2, -3, 3840, 673, 41, 91, 42245, 141, 44806, 166, 40967]}, 'GLZN': {'d': 2, 'p': 44, 'gens': [2486917, 1959255, 766665, 1487589, 1788885, 129251, 152393, 86153]}, 'Perm': {'d': 24, 'gens': [207174410831405123280, 25959064782933263450160, 55134438469733855232000, 33, 25959064782932176896000, 1614937680, 82256781831753424896000, 1394852659200]}}, 'schur_multiplier': [2, 2, 4], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 20], 'solvability_type': 7, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': '(C_2\\times C_{60}):Q_8', 'transitive_degree': 960, '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': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 2, 'aut_exponent': 4, 'aut_gen_orders': [2, 4], 'aut_gens': [[1, 2], [1, 6], [3, 2]], 'aut_group': '8.3', 'aut_hash': 3, 'aut_nilpotency_class': 2, 'aut_nilpotent': True, 'aut_order': 8, 'aut_permdeg': 4, 'aut_perms': [5, 9], 'aut_phi_ratio': 2.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 2, 1], [4, 2, 1, 1]], 'aut_supersolvable': True, 'aut_tex': 'D_4', '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': True, 'autcentquo_cyclic': True, 'autcentquo_exponent': 2, 'autcentquo_group': '2.1', 'autcentquo_hash': 1, 'autcentquo_nilpotent': True, 'autcentquo_order': 2, 'autcentquo_solvable': True, 'autcentquo_supersolvable': True, 'autcentquo_tex': 'C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 2, 2], [4, 2, 1]], 'center_label': '2.1', 'center_order': 2, 'central_product': False, 'central_quotient': '4.2', 'commutator_count': 1, 'commutator_label': '2.1', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1'], 'composition_length': 3, 'conjugacy_classes_known': True, 'counter': 3, 'cyclic': False, 'derived_length': 2, 'dihedral': True, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 2, 1, 2], [4, 2, 1, 1]], 'element_repr_type': 'PC', 'elementary': 2, 'eulerian_function': 3, 'exponent': 4, 'exponents_of_order': [3], 'factors_of_aut_order': [2], 'factors_of_order': [2], 'faithful_reps': [[2, 1, 1]], 'familial': True, 'frattini_label': '2.1', 'frattini_quotient': '4.2', 'hash': 3, 'hyperelementary': 2, 'inner_abelian': True, 'inner_cyclic': False, 'inner_exponent': 2, 'inner_gen_orders': [2, 2], 'inner_gens': [[1, 6], [5, 2]], 'inner_hash': 2, 'inner_nilpotent': True, 'inner_order': 4, 'inner_split': True, 'inner_tex': 'C_2^2', 'inner_used': [1, 2], 'irrC_degree': 2, 'irrQ_degree': 2, 'irrQ_dim': 2, 'irrR_degree': 2, 'irrep_stats': [[1, 4], [2, 1]], 'label': '8.3', 'linC_count': 1, 'linC_degree': 2, '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': 'D4', 'ngens': 2, 'nilpotency_class': 2, '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': 5, 'number_divisions': 5, 'number_normal_subgroups': 6, 'number_subgroup_autclasses': 6, 'number_subgroup_classes': 8, 'number_subgroups': 10, 'old_label': None, 'order': 8, 'order_factorization_type': 3, 'order_stats': [[1, 1], [2, 5], [4, 2]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 2, 'outer_gen_orders': [2], 'outer_gen_pows': [2], 'outer_gens': [[3, 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': 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], [2, 1]], 'representations': {'PC': {'code': 294, 'gens': [1, 2], 'pres': [3, -2, 2, -2, 37, 16]}, 'GLZ': {'b': 3, 'd': 2, 'gens': [14, 46]}, 'Lie': [{'d': 2, 'q': 3, 'gens': [29, 56, 24], 'family': 'COPlus'}, {'d': 1, 'q': 4, 'gens': [7, 16, 1], 'family': 'ASigmaL'}], 'GLFp': {'d': 2, 'p': 3, 'gens': [12, 55, 56]}, 'Perm': {'d': 4, 'gens': [6, 16, 7]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 3, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': True, 'sylow_subgroups_known': True, 'tex_name': 'D_4', 'transitive_degree': 4, 'wreath_data': ['C_2', 'C_2', '2T1'], 'wreath_product': True}
