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gps_subgroup_search • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'ambient': '4840.bq', 'ambient_counter': 43, 'ambient_order': 4840, 'ambient_tex': 'C_2\\times C_{11}^2:D_{10}', 'central': False, 'central_factor': True, 'centralizer_order': 2, 'characteristic': False, 'core_order': 2420, 'counter': 6, 'cyclic': False, 'direct': True, 'hall': 0, 'label': '4840.bq.2.c1.b1', 'maximal': True, 'maximal_normal': True, 'metabelian': False, 'metacyclic': False, 'minimal': False, 'minimal_normal': False, 'nilpotent': False, 'normal': True, 'old_label': '2.c1.b1', 'outer_equivalence': False, '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': '2420.bl', 'subgroup_hash': 9093935420212273711, 'subgroup_order': 2420, 'subgroup_tex': 'C_{11}^2:D_{10}', 'supersolvable': False, 'sylow': 0}
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gps_subgroup_data • Show schema
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{'ambient': '4840.bq', 'aut_centralizer_order': 1, 'aut_label': '2.c1', 'aut_quo_index': 1, 'aut_stab_index': 4, 'aut_weyl_group': '24200.bg', 'aut_weyl_index': 4, 'centralizer': '2420.a1.a1', 'complements': ['2420.a1.a1', '2420.c1.b1', '2420.b1.b1', '2420.b1.d1'], 'conjugacy_class_count': 1, 'contained_in': ['1.a1.a1'], 'contains': ['4.b1.a1', '4.b1.c1', '4.c1.a1', '10.c1.b1', '242.c1.b1'], 'core': '2.c1.b1', 'coset_action_label': None, 'count': 1, 'diagramx': [4597, 1200, 4803, 6721, 3676, 1008, 4147, 8287], 'generators': [2201, 564, 4440, 10, 440], 'label': '4840.bq.2.c1.b1', 'mobius_quo': 0, 'mobius_sub': -1, 'normal_closure': '2.c1.b1', 'normal_contained_in': ['1.a1.a1'], 'normal_contains': ['4.b1.a1', '4.b1.c1', '4.c1.a1'], 'normalizer': '1.a1.a1', 'old_label': '2.c1.b1', 'projective_image': '4840.bq', 'quotient_action_image': '1.1', 'quotient_action_kernel': '2.1', 'quotient_action_kernel_order': 2, 'quotient_fusion': None, 'short_label': '2.c1.b1', 'subgroup_fusion': None, 'weyl_group': '2420.bl'}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '4.2', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [22, 10, 110, 11], 'aut_gens': [[1, 2, 20, 220], [2021, 78, 740, 1660], [1105, 2342, 340, 440], [327, 722, 1680, 220], [761, 602, 20, 220]], 'aut_group': '24200.bg', 'aut_hash': 3957277396302200749, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 24200, 'aut_permdeg': 110, 'aut_perms': [4162428150886816161178240151199151181462697811485955374951452432011430524734565848228052174733400899590890070263022316021688199362491061810684555197700072933532498755411974045561, 8143141080032164825652563400804291297314032683202453524964488274481813539436593616742499849305557074033577325012555739559616187578512887415548989323270998965904574661713771508597, 5374547672368375436767410800054875967585176980801403118324541122727645013068783009557315124119944504000362582884049308372013584109299909888609251276932894880333302187870383355644, 5639589951477495536385032536073486278279475567229333903081645516978894202643868527459896083979687255991938369835297339175800574324213970477709559604713604974901921901777497076338], 'aut_phi_ratio': 27.5, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 55, 2, 1], [2, 121, 1, 1], [5, 242, 1, 2], [10, 242, 1, 2], [11, 10, 10, 1], [11, 20, 1, 1], [22, 110, 10, 1]], 'aut_supersolvable': False, 'aut_tex': 'F_{11}\\wr C_2', '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': False, 'autcentquo_cyclic': False, 'autcentquo_exponent': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 55, 2], [2, 121, 1], [5, 242, 2], [10, 242, 2], [11, 10, 10], [11, 20, 1], [22, 110, 10]], 'center_label': '1.1', 'center_order': 1, 'central_product': False, 'central_quotient': '2420.bl', 'commutator_count': 1, 'commutator_label': '605.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 5, 'conjugacy_classes_known': True, 'counter': 38, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [], 'direct_product': False, 'div_stats': [[1, 1, 1, 1], [2, 55, 1, 2], [2, 121, 1, 1], [5, 242, 2, 1], [10, 242, 2, 1], [11, 10, 5, 2], [11, 20, 1, 1], [22, 110, 5, 2]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 72, 'exponent': 110, 'exponents_of_order': [2, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 20], [20, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '2420.bl', 'hash': 9093935420212273711, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [22, 10, 11, 11], 'inner_gens': [[1, 1138, 1900, 980], [1265, 2, 340, 440], [761, 2322, 20, 220], [1881, 2202, 20, 220]], 'inner_hash': 9093935420212273711, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': True, 'inner_tex': 'C_{11}^2:D_{10}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 10, 'irrep_stats': [[1, 4], [2, 4], [10, 20], [20, 1]], 'label': '2420.bl', 'linC_count': 20, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 20, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C11^2:D10', 'ngens': 5, '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': 10, 'number_characteristic_subgroups': 6, 'number_conjugacy_classes': 29, 'number_divisions': 11, 'number_normal_subgroups': 8, 'number_subgroup_autclasses': 25, 'number_subgroup_classes': 34, 'number_subgroups': 1882, 'old_label': None, 'order': 2420, 'order_factorization_type': 222, 'order_stats': [[1, 1], [2, 231], [5, 484], [10, 484], [11, 120], [22, 1100]], 'outer_abelian': True, 'outer_cyclic': True, 'outer_equivalence': False, 'outer_exponent': 10, 'outer_gen_orders': [10], 'outer_gen_pows': [190], 'outer_gens': [[391, 598, 1640, 1360]], 'outer_group': '10.2', 'outer_hash': 2, 'outer_nilpotent': True, 'outer_order': 10, 'outer_permdeg': 7, 'outer_perms': [810], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_{10}', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 22, 'pgroup': 0, 'primary_abelian_invariants': [2, 2], 'quasisimple': False, 'rank': 2, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 4], [4, 2], [20, 1], [50, 4]], 'representations': {'PC': {'code': '14049809012149488505364556790032766700399', 'gens': [1, 2, 4, 5], 'pres': [5, -2, -2, -5, -11, 11, 9600, 11381, 26, 4442, 38003, 3408, 9113, 24504, 5509, 5514]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [33754893209411567, 19953910603511656, 11505406183563675, 9033174481858351, 38628134043324995]}, 'Perm': {'d': 22, 'gens': [51118820503597112497, 109635490173617790341, 10231460929669477779, 63661429115831947765, 168635168745471800936]}}, 'schur_multiplier': [2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_{11}^2:D_{10}', 'transitive_degree': 22, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'Agroup': True, 'Zgroup': False, 'abelian': False, 'abelian_quotient': '8.5', 'all_subgroups_known': True, 'almost_simple': False, 'aut_abelian': False, 'aut_cyclic': False, 'aut_derived_length': 3, 'aut_exponent': 220, 'aut_gen_orders': [10, 20, 10, 10], 'aut_gens': [[1, 2, 20, 440], [367, 2362, 180, 3400], [2963, 2062, 300, 2760], [2545, 578, 1220, 2440], [4421, 1342, 340, 2640]], 'aut_group': None, 'aut_hash': 4512992591201935324, 'aut_nilpotency_class': -1, 'aut_nilpotent': False, 'aut_order': 96800, 'aut_permdeg': 220, 'aut_perms': [13902313161652451538561635301240000754961373570221945425734899030669798866512916942787215583610862888588959815681942513393445770495733390672884191943254122754379511032322443175181560764664928978844488612288946996610867398920825125359023008482895287234330353431079659631046431739387893015513996813354804344427829487132017134073016679559298190942481241964621663214791207597942509492852212932914667657812003014056678333816776, 16429703857574820854226954218794125490904834941354524395858788818996996645162637161387682528241727662242081985632182731554416168614627152064634596830211433062296180977840093029328139006211935063917828862017366658284729882930085711017167405750374285792170866810420064772097412673105284255019816184652957583943333839522903072153222006832343670956399136082894117049521796326842477306073964970068121695828203297717080538833580, 18559670801904573743532229009321488193340238726224176687274977197182324675523914179945238260112625266178159470608043871497996391139642544767615069120268036821120268457462122263262552912640820859947487329945262042767338275788047660142700085277562628482572776329515950815860728402747860222448998157230434095506479431785538703994064834390733449755685573871042480817687677519036977819479474692302735095236073913473694106325797, 11300255942286713618872660318020341410503743758652047132018672874126017395661799697052919033800539864403936416738304033222030131911492551242341285315987006692992028369933655673274890125051817501791418338799067141962169165515489160374485292820576228902314154954402836058053998546251293985809772463840857795195764469627940454581112582059820231527849235665969233786696398753042959030472516367708824044201391242515103097763], 'aut_phi_ratio': 55.0, 'aut_solvable': True, 'aut_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 55, 4, 1], [2, 121, 2, 1], [5, 242, 1, 2], [10, 242, 1, 2], [10, 242, 2, 2], [11, 10, 10, 1], [11, 20, 1, 1], [22, 10, 10, 1], [22, 20, 1, 1], [22, 110, 20, 1]], 'aut_supersolvable': False, 'aut_tex': 'C_{11}^2.C_{10}^2.C_2^3', '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': 220, 'autcentquo_group': '24200.bg', 'autcentquo_hash': 3957277396302200749, 'autcentquo_nilpotent': False, 'autcentquo_order': 24200, 'autcentquo_solvable': True, 'autcentquo_supersolvable': False, 'autcentquo_tex': 'F_{11}\\wr C_2', 'cc_stats': [[1, 1, 1], [2, 1, 1], [2, 55, 4], [2, 121, 2], [5, 242, 2], [10, 242, 6], [11, 10, 10], [11, 20, 1], [22, 10, 10], [22, 20, 1], [22, 110, 20]], 'center_label': '2.1', 'center_order': 2, 'central_product': True, 'central_quotient': '2420.bl', 'commutator_count': 1, 'commutator_label': '605.6', 'complements_known': True, 'complete': False, 'complex_characters_known': True, 'composition_factors': ['2.1', '2.1', '2.1', '5.1', '11.1', '11.1'], 'composition_length': 6, 'conjugacy_classes_known': True, 'counter': 43, 'cyclic': False, 'derived_length': 3, 'dihedral': False, 'direct_factorization': [['2.1', 1], ['2420.bl', 1]], 'direct_product': True, 'div_stats': [[1, 1, 1, 1], [2, 1, 1, 1], [2, 55, 1, 4], [2, 121, 1, 2], [5, 242, 2, 1], [10, 242, 2, 3], [11, 10, 5, 2], [11, 20, 1, 1], [22, 10, 5, 2], [22, 20, 1, 1], [22, 110, 5, 4]], 'element_repr_type': 'PC', 'elementary': 1, 'eulerian_function': 368928, 'exponent': 110, 'exponents_of_order': [3, 2, 1], 'factors_of_aut_order': [2, 5, 11], 'factors_of_order': [2, 5, 11], 'faithful_reps': [[10, 1, 20], [20, 1, 1]], 'familial': False, 'frattini_label': '1.1', 'frattini_quotient': '4840.bq', 'hash': 6953430380680834955, 'hyperelementary': 1, 'inner_abelian': False, 'inner_cyclic': False, 'inner_exponent': 110, 'inner_gen_orders': [22, 10, 11, 11], 'inner_gens': [[1, 3058, 3500, 440], [1365, 2, 380, 3240], [1801, 82, 20, 440], [1, 2482, 20, 440]], 'inner_hash': 9093935420212273711, 'inner_nilpotent': False, 'inner_order': 2420, 'inner_split': True, 'inner_tex': 'C_{11}^2:D_{10}', 'inner_used': [1, 2], 'irrC_degree': 10, 'irrQ_degree': 20, 'irrQ_dim': 20, 'irrR_degree': 10, 'irrep_stats': [[1, 8], [2, 8], [10, 40], [20, 2]], 'label': '4840.bq', 'linC_count': 20, 'linC_degree': 10, 'linFp_degree': None, 'linFq_degree': None, 'linQ_degree': 20, 'linQ_degree_count': 1, 'linQ_dim': 20, 'linQ_dim_count': 1, 'linR_count': 20, 'linR_degree': 10, 'maximal_subgroups_known': True, 'metabelian': False, 'metacyclic': False, 'monomial': True, 'name': 'C2*C11^2:D10', '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], 'normal_index_bound': 0, 'normal_order_bound': 0, 'normal_subgroups_known': True, 'number_autjugacy_classes': 15, 'number_characteristic_subgroups': 9, 'number_conjugacy_classes': 58, 'number_divisions': 22, 'number_normal_subgroups': 23, 'number_subgroup_autclasses': 50, 'number_subgroup_classes': 106, 'number_subgroups': 7172, 'old_label': None, 'order': 4840, 'order_factorization_type': 321, 'order_stats': [[1, 1], [2, 463], [5, 484], [10, 1452], [11, 120], [22, 2320]], 'outer_abelian': False, 'outer_cyclic': False, 'outer_equivalence': False, 'outer_exponent': 20, 'outer_gen_orders': [2, 20], 'outer_gen_pows': [0, 0], 'outer_gens': [[4401, 582, 420, 4400], [1551, 3462, 260, 4160]], 'outer_group': '40.10', 'outer_hash': 10, 'outer_nilpotent': True, 'outer_order': 40, 'outer_permdeg': 9, 'outer_perms': [5040, 81450], 'outer_solvable': True, 'outer_supersolvable': True, 'outer_tex': 'C_5\\times D_4', 'pc_rank': 4, 'perfect': False, 'permutation_degree': 24, 'pgroup': 0, 'primary_abelian_invariants': [2, 2, 2], 'quasisimple': False, 'rank': 3, 'rational': False, 'rational_characters_known': True, 'ratrep_stats': [[1, 8], [4, 4], [20, 2], [50, 8]], 'representations': {'PC': {'code': '10226572294142386636846379093953539386210002016532971003099', 'gens': [1, 2, 4, 6], 'pres': [6, -2, -2, -5, -2, -11, 11, 2640, 36697, 31, 80210, 84003, 4569, 1095, 69, 51604, 4810, 2716, 58331, 21617]}, 'GLFp': {'d': 4, 'p': 11, 'gens': [12612561237093724, 9033174481858351, 11916568804832820, 30590792246403079, 39039296666365701, 41772741070013040]}, 'Perm': {'d': 24, 'gens': [4769522350099504399488, 55142383550512012005751, 28317401381289600823921]}}, 'schur_multiplier': [2, 2, 2], 'semidirect_product': True, 'simple': False, 'smith_abelian_invariants': [2, 2, 2], 'solvability_type': 11, 'solvable': True, 'subgroup_inclusions_known': True, 'subgroup_index_bound': 0, 'supersolvable': False, 'sylow_subgroups_known': True, 'tex_name': 'C_2\\times C_{11}^2:D_{10}', 'transitive_degree': 44, 'wreath_data': None, 'wreath_product': False}
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gps_groups • Show schema
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{'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}
